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Номер 39.2, страница 271 - гдз по физике 10-11 класс задачник Гельфгат, Генденштейн
Авторы: Гельфгат И. М., Генденштейн Л. Э., Кирик Л. А.
Тип: Задачник
Издательство: Илекса
Год издания: 2008 - 2026
Уровень обучения: профильный
Цвет обложки: красный лупа, парень едет на велосипеде
ISBN: 978-5-89237-252-7
Популярные ГДЗ в 10 классе
Квантовая физика. 39. Световые кванты. Упражнения - номер 39.2, страница 271.
App\Models\Task {#1030 // resources/views/models/task/default.blade.php #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1319834 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "271" "field_page_end" => null "field_url" => "/10-klass/fizika/gelfgat-zadachnik/39-2" "field_display_title" => "39.2" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037 #items: array:1 [ 0 => App\Models\Term {#1036 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #original: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1035 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1046 #items: array:1 [ 0 => App\Models\Branch {#1045 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1319386 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Квантовая физика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1047 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "271" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1081 #items: array:1 [ 0 => App\Models\Book {#1048 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 5400 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1050 #items: array:1 [ 0 => App\Models\Term {#1049 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6493 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Физика" "field_abbreviated_name" => null "field_cases" => array:6 [ "field_accusative_case" => "физику" "field_creative_case" => "физикой" "field_dative_case" => "физике" "field_genitive_case" => "физики" "field_nominative_case" => "физика" "field_prepositional_case" => "физике" ] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "fizika" ] #original: array:10 [ "id" => 6493 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Физика" "field_abbreviated_name" => null "field_cases" => array:6 [ "field_accusative_case" => "физику" "field_creative_case" => "физикой" "field_dative_case" => "физике" "field_genitive_case" => "физики" "field_nominative_case" => "физика" "field_prepositional_case" => "физике" ] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "fizika" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1051 #items: array:2 [ 0 => App\Models\Term {#1052 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5459 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "10" "field_cases" => array:6 [ "field_accusative_case" => "десятый" "field_creative_case" => "десятым" "field_dative_case" => "десятому" "field_genitive_case" => "десятого" "field_nominative_case" => "десятый" "field_prepositional_case" => "десятом" ] "field_translit" => "desjatyj" ] #original: array:6 [ "id" => 5459 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "10" "field_cases" => array:6 [ "field_accusative_case" => "десятый" "field_creative_case" => "десятым" "field_dative_case" => "десятому" "field_genitive_case" => "десятого" "field_nominative_case" => "десятый" "field_prepositional_case" => "десятом" ] "field_translit" => "desjatyj" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Term {#1053 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5460 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "11" "field_cases" => array:6 [ "field_accusative_case" => "одиннадцатый" "field_creative_case" => "одиннадцатым" "field_dative_case" => "одиннадцатому" "field_genitive_case" => "одинадцатого" "field_nominative_case" => "одинадцатый" "field_prepositional_case" => "одиннадцатом" ] "field_translit" => "odinadcatyj" ] #original: array:6 [ "id" => 5460 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "11" "field_cases" => array:6 [ "field_accusative_case" => "одиннадцатый" "field_creative_case" => "одиннадцатым" "field_dative_case" => "одиннадцатому" "field_genitive_case" => "одинадцатого" "field_nominative_case" => "одинадцатый" "field_prepositional_case" => "одиннадцатом" ] "field_translit" => "odinadcatyj" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1054 #items: array:1 [ 0 => App\Models\Term {#1055 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5158 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Илекса" "field_cases" => null "field_translit" => "ileksa" ] #original: array:6 [ "id" => 5158 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Илекса" "field_cases" => null "field_translit" => "ileksa" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1056 #items: array:3 [ 0 => App\Models\Term {#1057 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 4102 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Гельфгат" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Илья" "field_patronymic" => "Маркович" "field_surname_rp" => null ] #original: array:12 [ "id" => 4102 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Гельфгат" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Илья" "field_patronymic" => "Маркович" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Term {#1058 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 4104 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Генденштейн" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Лев" "field_patronymic" => "Элевич" "field_surname_rp" => "Генденштейна" ] #original: array:12 [ "id" => 4104 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Генденштейн" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Лев" "field_patronymic" => "Элевич" "field_surname_rp" => "Генденштейна" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Term {#1059 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 4583 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Кирик" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Леонид" "field_patronymic" => "Анатольевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 4583 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Кирик" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Леонид" "field_patronymic" => "Анатольевич" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1060 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1061 #items: array:1 [ 0 => App\Models\Term {#1062 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6518 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Задачник" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "задачник" "field_creative_case" => "задачником" "field_dative_case" => "задачнику" "field_genitive_case" => "задачника" "field_nominative_case" => "задачник" "field_prepositional_case" => "задачнике" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "zadachnik" ] #original: array:10 [ "id" => 6518 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Задачник" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "задачник" "field_creative_case" => "задачником" "field_dative_case" => "задачнику" "field_genitive_case" => "задачника" "field_nominative_case" => "задачник" "field_prepositional_case" => "задачнике" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "zadachnik" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1063 #items: array:1 [ 0 => App\Models\Term {#1064 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 9 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Россия" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "rossiya" ] #original: array:6 [ "id" => 9 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Россия" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "rossiya" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1065 #items: array:1 [ 0 => App\Models\Term {#1066 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 15 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Москва" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "moskva" ] #original: array:6 [ "id" => 15 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Москва" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "moskva" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1067 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1068 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1069 #items: array:1 [ 0 => App\Models\Term {#1070 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 40 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "профильный" "field_cases" => array:6 [ "field_accusative_case" => "профильный" "field_creative_case" => "профильным" "field_dative_case" => "профильному" "field_genitive_case" => "профильного" "field_nominative_case" => "профильный" "field_prepositional_case" => "профильном" ] "field_translit" => "profilnyy" ] #original: array:6 [ "id" => 40 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "профильный" "field_cases" => array:6 [ "field_accusative_case" => "профильный" "field_creative_case" => "профильным" "field_dative_case" => "профильному" "field_genitive_case" => "профильного" "field_nominative_case" => "профильный" "field_prepositional_case" => "профильном" ] "field_translit" => "profilnyy" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1071 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1072 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1073 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => "лупа, парень едет на велосипеде" "field_publication_year" => "2008" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "459" "field_priority" => null "field_default_folder" => "/fizika_10/gelfgat-z/" "field_isbn" => "978-5-89237-252-7" "field_cover" => array:1 [ 0 => "/media/fizika_10/gelfgat-z/covers/cover1.webp?ts=1756049816" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_10/gelfgat-z/covers/cover1.webp?ts=1756049816" "alt" => "" "width" => "1566" "height" => "2412" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1074 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1075 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1076 #items: [] #escapeWhenCastingToString: false } "field_url" => "/10-klass/fizika/gelfgat-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1077 #items: array:1 [ 0 => App\Models\Term {#1078 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 46 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "красный" "field_cases" => array:6 [ "field_accusative_case" => "красный" "field_creative_case" => "красным" "field_dative_case" => "красному" "field_genitive_case" => "красного" "field_nominative_case" => "красный" "field_prepositional_case" => "красном" ] "field_translit" => "krasnyy" ] #original: array:6 [ "id" => 46 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "красный" "field_cases" => array:6 [ "field_accusative_case" => "красный" "field_creative_case" => "красным" "field_dative_case" => "красному" "field_genitive_case" => "красного" "field_nominative_case" => "красный" "field_prepositional_case" => "красном" ] "field_translit" => "krasnyy" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 381 "subject" => 556 "class_subject" => 494 ] ] #original: array:50 [ "id" => 5400 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1050} "field_class" => Illuminate\Database\Eloquent\Collection {#1051} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1054} "field_author" => Illuminate\Database\Eloquent\Collection {#1056} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1060} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1061} "field_country" => Illuminate\Database\Eloquent\Collection {#1063} "field_city" => Illuminate\Database\Eloquent\Collection {#1065} "field_series" => Illuminate\Database\Eloquent\Collection {#1067} "field_umk" => Illuminate\Database\Eloquent\Collection {#1068} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1069} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1071} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1072} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1073} "field_under_the_edition_degree" => null "field_cover_description" => "лупа, парень едет на велосипеде" "field_publication_year" => "2008" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "459" "field_priority" => null "field_default_folder" => "/fizika_10/gelfgat-z/" "field_isbn" => "978-5-89237-252-7" "field_cover" => array:1 [ 0 => "/media/fizika_10/gelfgat-z/covers/cover1.webp?ts=1756049816" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_10/gelfgat-z/covers/cover1.webp?ts=1756049816" "alt" => "" "width" => "1566" "height" => "2412" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1074} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1075} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1076} "field_url" => "/10-klass/fizika/gelfgat-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1077} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 381 "subject" => 556 "class_subject" => 494 ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1079 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1319386 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Квантовая физика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1047} "field_page_start" => "271" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1081} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1079} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1110 #items: array:3 [ 0 => App\Models\Branch {#1120 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1319386 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Квантовая физика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1121 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "271" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1122 #items: array:1 [ 0 => App\Models\Book {#1048} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1123 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1319386 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Квантовая физика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1121} "field_page_start" => "271" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1122} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1123} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Branch {#1124 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1319387 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "39. Световые кванты" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1125 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "271" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1126 #items: array:1 [ 0 => App\Models\Book {#1048} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1127 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1319387 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "39. Световые кванты" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1125} "field_page_start" => "271" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1126} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1127} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Branch {#1128 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1319388 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Упражнения" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1129 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "271" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1130 #items: array:1 [ 0 => App\Models\Book {#1048} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1139 #items: array:1 [ 0 => App\Models\Branch {#1138 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1319387 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "39. Световые кванты" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1140 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "271" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1141 #items: array:1 [ 0 => App\Models\Book {#1048} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1142 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1319387 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "39. Световые кванты" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1140} "field_page_start" => "271" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1141} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1142} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1319388 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Упражнения" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1129} "field_page_start" => "271" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1130} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1139} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1038 #items: array:2 [ 0 => App\Models\Element {#1102 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 1493969 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1093 #items: array:1 [ 0 => App\Models\Edition {#1092 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 5430 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1085 #items: array:1 [ 0 => App\Models\Term {#1090 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5158 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Илекса" "field_cases" => null "field_translit" => "ileksa" ] #original: array:6 [ "id" => 5158 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Илекса" "field_cases" => null "field_translit" => "ileksa" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1083 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1091 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1088 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 5430 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1085} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1083} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1091} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1088} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1319834" "type" => "task" ] "text" => "<p><strong>39.2.</strong> Для калия красная граница фотоэффекта равна $\lambda_{max} = 0,62 \text{ мкм}$. Какую максимальную скорость $\upsilon$ могут иметь фотоэлектроны, вылетающие при облучении калия фиолетовым светом с длиной волны $\lambda = 0,42 \text{ мкм}$?</p><p>☑ $\upsilon = 580 \text{ км/с}$.</p><p><strong><em>Решение.</em></strong> Работа выхода совпадает с минимальной энергией фотона, вызывающего фотоэффект: $A = hc/\lambda_{max}$. Тогда из уравнения Эйнштейна для фотоэффекта следует:</p><p>$\upsilon = \sqrt{\frac{2hc(\lambda_{max} - \lambda)}{m\lambda\lambda_{max}}} = 5,8 \cdot 10^5 \text{ (м/с)}$.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "2-1.jpg" "alt" => null "width" => "1391" "height" => 686 "path" => "/media/fizika_10/gelfgat-z/0-39/2-1.webp?ts=1756251158" ] ] ] #original: array:7 [ "id" => 1493969 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1093} "task" => array:2 [ "refs" => "1319834" "type" => "task" ] "text" => "<p><strong>39.2.</strong> Для калия красная граница фотоэффекта равна $\lambda_{max} = 0,62 \text{ мкм}$. Какую максимальную скорость $\upsilon$ могут иметь фотоэлектроны, вылетающие при облучении калия фиолетовым светом с длиной волны $\lambda = 0,42 \text{ мкм}$?</p><p>☑ $\upsilon = 580 \text{ км/с}$.</p><p><strong><em>Решение.</em></strong> Работа выхода совпадает с минимальной энергией фотона, вызывающего фотоэффект: $A = hc/\lambda_{max}$. Тогда из уравнения Эйнштейна для фотоэффекта следует:</p><p>$\upsilon = \sqrt{\frac{2hc(\lambda_{max} - \lambda)}{m\lambda\lambda_{max}}} = 5,8 \cdot 10^5 \text{ (м/с)}$.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "2-1.jpg" "alt" => null "width" => "1391" "height" => 686 "path" => "/media/fizika_10/gelfgat-z/0-39/2-1.webp?ts=1756251158" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Element {#1100 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1691526 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1086 #items: array:1 [ 0 => App\Models\Edition {#1084 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 6138 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1043 #items: array:1 [ 0 => App\Models\Term {#1041 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 7012 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Gemini 2.5 Pro" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "gemini 2.5 pro" ] #original: array:6 [ "id" => 7012 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Gemini 2.5 Pro" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "gemini 2.5 pro" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1116 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1082 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1034 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 6138 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1043} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1116} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1082} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1034} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1319834" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Красная граница фотоэффекта для калия, $ \lambda_{max} = 0,62 \text{ мкм} = 0,62 \cdot 10^{-6} \text{ м} $</p><p>Длина волны падающего фиолетового света, $ \lambda = 0,42 \text{ мкм} = 0,42 \cdot 10^{-6} \text{ м} $</p><p>Постоянная Планка, $ h \approx 6,63 \cdot 10^{-34} \text{ Дж} \cdot \text{с} $</p><p>Скорость света в вакууме, $ c \approx 3 \cdot 10^8 \text{ м/с} $</p><p>Масса электрона, $ m_e \approx 9,11 \cdot 10^{-31} \text{ кг} $</p><p><strong>Найти:</strong></p><p>Максимальную скорость фотоэлектронов $ v $.</p><p><strong>Решение:</strong></p><p>Для решения задачи используется уравнение Эйнштейна для фотоэффекта, которое связывает энергию падающего фотона, работу выхода электрона из металла и максимальную кинетическую энергию вылетевшего электрона:</p><p>$ E_{photon} = A_{вых} + E_{k, max} $</p><p>Энергия падающего фотона ($ E_{photon} $) определяется его длиной волны $ \lambda $ по формуле:</p><p>$ E_{photon} = \frac{hc}{\lambda} $</p><p>Работа выхода ($ A_{вых} $) — это минимальная энергия, которую нужно сообщить электрону, чтобы он покинул металл. Эта энергия соответствует энергии фотона с длиной волны, равной красной границе фотоэффекта ($ \lambda_{max} $):</p><p>$ A_{вых} = \frac{hc}{\lambda_{max}} $</p><p>Максимальная кинетическая энергия ($ E_{k, max} $) фотоэлектрона связана с его максимальной скоростью $ v $ соотношением:</p><p>$ E_{k, max} = \frac{m_e v^2}{2} $</p><p>Подставим все эти выражения в исходное уравнение Эйнштейна:</p><p>$ \frac{hc}{\lambda} = \frac{hc}{\lambda_{max}} + \frac{m_e v^2}{2} $</p><p>Выразим из этого уравнения член, содержащий кинетическую энергию:</p><p>$ \frac{m_e v^2}{2} = \frac{hc}{\lambda} - \frac{hc}{\lambda_{max}} $</p><p>Вынесем общий множитель $ hc $ за скобки и приведем дроби в скобках к общему знаменателю:</p><p>$ \frac{m_e v^2}{2} = hc \left( \frac{1}{\lambda} - \frac{1}{\lambda_{max}} \right) = hc \frac{\lambda_{max} - \lambda}{\lambda \lambda_{max}} $</p><p>Теперь выразим квадрат максимальной скорости $ v^2 $:</p><p>$ v^2 = \frac{2hc(\lambda_{max} - \lambda)}{m_e \lambda \lambda_{max}} $</p><p>Осталось извлечь квадратный корень, чтобы найти искомую скорость $ v $:</p><p>$ v = \sqrt{\frac{2hc(\lambda_{max} - \lambda)}{m_e \lambda \lambda_{max}}} $</p><p>Подставим числовые значения в полученную формулу:</p><p>$ v = \sqrt{\frac{2 \cdot (6,63 \cdot 10^{-34} \text{ Дж} \cdot \text{с}) \cdot (3 \cdot 10^8 \text{ м/с}) \cdot (0,62 \cdot 10^{-6} \text{ м} - 0,42 \cdot 10^{-6} \text{ м})}{(9,11 \cdot 10^{-31} \text{ кг}) \cdot (0,42 \cdot 10^{-6} \text{ м}) \cdot (0,62 \cdot 10^{-6} \text{ м})}} $</p><p>$ v = \sqrt{\frac{2 \cdot 6,63 \cdot 3 \cdot 10^{-26} \cdot (0,20 \cdot 10^{-6})}{9,11 \cdot 0,42 \cdot 0,62 \cdot 10^{-43}}} = \sqrt{\frac{7,956 \cdot 10^{-32}}{2,374 \cdot 10^{-43}}} $</p><p>$ v \approx \sqrt{3,351 \cdot 10^{11}} \text{ м/с} \approx 5,789 \cdot 10^5 \text{ м/с} $</p><p>Округлим результат до двух значащих цифр и переведем в километры в секунду ($ 1 \text{ км/с} = 1000 \text{ м/с} $):</p><p>$ v \approx 5,8 \cdot 10^5 \text{ м/с} = 580 \cdot 10^3 \text{ м/с} = 580 \text{ км/с} $</p><p><strong>Ответ:</strong> $ v \approx 580 \text{ км/с} $</p>" ] #original: array:6 [ "id" => 1691526 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1086} "task" => array:2 [ "refs" => "1319834" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Красная граница фотоэффекта для калия, $ \lambda_{max} = 0,62 \text{ мкм} = 0,62 \cdot 10^{-6} \text{ м} $</p><p>Длина волны падающего фиолетового света, $ \lambda = 0,42 \text{ мкм} = 0,42 \cdot 10^{-6} \text{ м} $</p><p>Постоянная Планка, $ h \approx 6,63 \cdot 10^{-34} \text{ Дж} \cdot \text{с} $</p><p>Скорость света в вакууме, $ c \approx 3 \cdot 10^8 \text{ м/с} $</p><p>Масса электрона, $ m_e \approx 9,11 \cdot 10^{-31} \text{ кг} $</p><p><strong>Найти:</strong></p><p>Максимальную скорость фотоэлектронов $ v $.</p><p><strong>Решение:</strong></p><p>Для решения задачи используется уравнение Эйнштейна для фотоэффекта, которое связывает энергию падающего фотона, работу выхода электрона из металла и максимальную кинетическую энергию вылетевшего электрона:</p><p>$ E_{photon} = A_{вых} + E_{k, max} $</p><p>Энергия падающего фотона ($ E_{photon} $) определяется его длиной волны $ \lambda $ по формуле:</p><p>$ E_{photon} = \frac{hc}{\lambda} $</p><p>Работа выхода ($ A_{вых} $) — это минимальная энергия, которую нужно сообщить электрону, чтобы он покинул металл. Эта энергия соответствует энергии фотона с длиной волны, равной красной границе фотоэффекта ($ \lambda_{max} $):</p><p>$ A_{вых} = \frac{hc}{\lambda_{max}} $</p><p>Максимальная кинетическая энергия ($ E_{k, max} $) фотоэлектрона связана с его максимальной скоростью $ v $ соотношением:</p><p>$ E_{k, max} = \frac{m_e v^2}{2} $</p><p>Подставим все эти выражения в исходное уравнение Эйнштейна:</p><p>$ \frac{hc}{\lambda} = \frac{hc}{\lambda_{max}} + \frac{m_e v^2}{2} $</p><p>Выразим из этого уравнения член, содержащий кинетическую энергию:</p><p>$ \frac{m_e v^2}{2} = \frac{hc}{\lambda} - \frac{hc}{\lambda_{max}} $</p><p>Вынесем общий множитель $ hc $ за скобки и приведем дроби в скобках к общему знаменателю:</p><p>$ \frac{m_e v^2}{2} = hc \left( \frac{1}{\lambda} - \frac{1}{\lambda_{max}} \right) = hc \frac{\lambda_{max} - \lambda}{\lambda \lambda_{max}} $</p><p>Теперь выразим квадрат максимальной скорости $ v^2 $:</p><p>$ v^2 = \frac{2hc(\lambda_{max} - \lambda)}{m_e \lambda \lambda_{max}} $</p><p>Осталось извлечь квадратный корень, чтобы найти искомую скорость $ v $:</p><p>$ v = \sqrt{\frac{2hc(\lambda_{max} - \lambda)}{m_e \lambda \lambda_{max}}} $</p><p>Подставим числовые значения в полученную формулу:</p><p>$ v = \sqrt{\frac{2 \cdot (6,63 \cdot 10^{-34} \text{ Дж} \cdot \text{с}) \cdot (3 \cdot 10^8 \text{ м/с}) \cdot (0,62 \cdot 10^{-6} \text{ м} - 0,42 \cdot 10^{-6} \text{ м})}{(9,11 \cdot 10^{-31} \text{ кг}) \cdot (0,42 \cdot 10^{-6} \text{ м}) \cdot (0,62 \cdot 10^{-6} \text{ м})}} $</p><p>$ v = \sqrt{\frac{2 \cdot 6,63 \cdot 3 \cdot 10^{-26} \cdot (0,20 \cdot 10^{-6})}{9,11 \cdot 0,42 \cdot 0,62 \cdot 10^{-43}}} = \sqrt{\frac{7,956 \cdot 10^{-32}}{2,374 \cdot 10^{-43}}} $</p><p>$ v \approx \sqrt{3,351 \cdot 10^{11}} \text{ м/с} \approx 5,789 \cdot 10^5 \text{ м/с} $</p><p>Округлим результат до двух значащих цифр и переведем в километры в секунду ($ 1 \text{ км/с} = 1000 \text{ м/с} $):</p><p>$ v \approx 5,8 \cdot 10^5 \text{ м/с} = 580 \cdot 10^3 \text{ м/с} = 580 \text{ км/с} $</p><p><strong>Ответ:</strong> $ v \approx 580 \text{ км/с} $</p>" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1319835" "type" => "task" ] "previous" => array:2 [ "refs" => "1319833" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1105 #items: array:1 [ 0 => App\Models\Book {#1048} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1042 #items: array:1 [ 0 => App\Models\BookPage {#1107 #connection: "mysql" #table: "book_pages" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 1341232 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "271" "field_url" => "/10-klass/fizika/gelfgat-zadachnik/page-271" "field_display_title" => "271" "field_folder" => "1" "field_image_name" => "271" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1101 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1096 #items: array:1 [ 0 => App\Models\Book {#1048} ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "edition_groups" => Illuminate\Database\Eloquent\Collection {#1098 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1112 #items: array:1 [ 0 => App\Models\Element {#1114 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1519777 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1113 #items: array:1 [ 0 => App\Models\Edition {#1092} ] #escapeWhenCastingToString: false } "book_page" => array:2 [ "refs" => "1341232" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "271-1.jpg" "alt" => null "width" => "1548" "height" => 2469 "path" => "/media/fizika_10/gelfgat-z/0-1/271-1.webp?ts=1756642419" ] ] ] #original: array:6 [ "id" => 1519777 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1113} "book_page" => array:2 [ "refs" => "1341232" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "271-1.jpg" "alt" => null "width" => "1548" "height" => 2469 "path" => "/media/fizika_10/gelfgat-z/0-1/271-1.webp?ts=1756642419" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1341233" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1341231" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1206 #items: array:3 [ 0 => App\Models\Task {#1216 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1319833 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "271" "field_page_end" => null "field_url" => "/10-klass/fizika/gelfgat-zadachnik/39-1" "field_display_title" => "39.1" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1217 #items: array:1 [ 0 => App\Models\Term {#1036} ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1218 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1219 #items: array:1 [ 0 => App\Models\Branch {#1120} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1220 #items: array:3 [ 0 => App\Models\Branch {#1120} 1 => App\Models\Branch {#1124} 2 => App\Models\Branch {#1128} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1222 #items: array:2 [ 0 => App\Models\Element {#1231 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 1493968 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1232 #items: array:1 [ …1] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1319833" "type" => "task" ] "text" => "<p><strong>39.1.</strong> Под каким напряжением $\text{U}$ работает рентгеновская трубка, если самое «жесткое» излучение в ее спектре имеет длину волны $\lambda_{\min} = 3,0 \cdot 10^{1}$ м?</p><p>☑ $U = 41$ кВ.</p><p><strong><em>Решение.</em></strong> Энергия излучаемого фотона $hv = hc/\lambda$ не может превышать полученной электроном при разгоне кинетической энергии $W_k = eU$.</p><p>Поэтому $\frac{hc}{\lambda_{\min}} = eU$ , откуда $U = \frac{hc}{e\lambda_{\min}} = 41$ (кВ).</p>" "img" => array:1 [ 0 => array:5 [ …5] ] ] #original: array:7 [ "id" => 1493968 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1232} "task" => array:2 [ "refs" => "1319833" "type" => "task" ] "text" => "<p><strong>39.1.</strong> Под каким напряжением $\text{U}$ работает рентгеновская трубка, если самое «жесткое» излучение в ее спектре имеет длину волны $\lambda_{\min} = 3,0 \cdot 10^{1}$ м?</p><p>☑ $U = 41$ кВ.</p><p><strong><em>Решение.</em></strong> Энергия излучаемого фотона $hv = hc/\lambda$ не может превышать полученной электроном при разгоне кинетической энергии $W_k = eU$.</p><p>Поэтому $\frac{hc}{\lambda_{\min}} = eU$ , откуда $U = \frac{hc}{e\lambda_{\min}} = 41$ (кВ).</p>" "img" => array:1 [ 0 => array:5 [ …5] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Element {#1233 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1691525 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1234 #items: array:1 [ …1] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1319833" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Минимальная длина волны рентгеновского излучения: $\lambda_{min} = 3,0 \cdot 10^{-11}$ м</p><p>Постоянная Планка: $h \approx 6,626 \cdot 10^{-34}$ Дж$\cdot$с</p><p>Скорость света в вакууме: $c \approx 3 \cdot 10^8$ м/с</p><p>Элементарный заряд: $e \approx 1,602 \cdot 10^{-19}$ Кл</p><p><strong>Найти:</strong></p><p>Напряжение $U$.</p><p><strong>Решение:</strong></p><p>В рентгеновской трубке электроны ускоряются электрическим полем с напряжением $U$. При этом они приобретают кинетическую энергию $W_k$, которая равна работе электрического поля:</p><p>$W_k = eU$</p><p>где $e$ — это элементарный заряд.</p><p>При резком торможении электронов об анод трубки их кинетическая энергия превращается в энергию рентгеновских фотонов. Самое «жесткое» излучение (излучение с максимальной энергией и, следовательно, с минимальной длиной волны $\lambda_{min}$) возникает в том случае, когда вся кинетическая энергия одного электрона полностью переходит в энергию одного испущенного фотона.</p><p>Энергия фотона $E_{ф}$ определяется формулой Планка:</p><p>$E_{ф} = h\nu = \frac{hc}{\lambda}$</p><p>где $h$ — постоянная Планка, $\nu$ — частота излучения, $c$ — скорость света, $\lambda$ — длина волны.</p><p>Согласно закону сохранения энергии, приравниваем максимальную энергию фотона (соответствующую $\lambda_{min}$) к кинетической энергии электрона:</p><p>$E_{ф_{max}} = W_k$</p><p>$\frac{hc}{\lambda_{min}} = eU$</p><p>Из этого соотношения выразим искомое напряжение $U$:</p><p>$U = \frac{hc}{e\lambda_{min}}$</p><p>Подставим числовые значения в систему СИ:</p><p>$U = \frac{6,626 \cdot 10^{-34} \text{ Дж}\cdot\text{с} \cdot 3 \cdot 10^8 \text{ м/с}}{1,602 \cdot 10^{-19} \text{ Кл} \cdot 3,0 \cdot 10^{-11} \text{ м}} \approx \frac{19,878 \cdot 10^{-26}}{4,806 \cdot 10^{-30}} \text{ В}$</p><p>$U \approx 4,136 \cdot 10^4 \text{ В}$</p><p>Переведем результат в киловольты, зная, что 1 кВ = $10^3$ В:</p><p>$U \approx 41,36 \text{ кВ}$</p><p>Округляя до целых, получаем $U \approx 41$ кВ.</p><p><strong>Ответ:</strong> Напряжение, под которым работает рентгеновская трубка, составляет приблизительно $41$ кВ.</p>" ] #original: array:6 [ "id" => 1691525 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1234} "task" => array:2 [ "refs" => "1319833" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Минимальная длина волны рентгеновского излучения: $\lambda_{min} = 3,0 \cdot 10^{-11}$ м</p><p>Постоянная Планка: $h \approx 6,626 \cdot 10^{-34}$ Дж$\cdot$с</p><p>Скорость света в вакууме: $c \approx 3 \cdot 10^8$ м/с</p><p>Элементарный заряд: $e \approx 1,602 \cdot 10^{-19}$ Кл</p><p><strong>Найти:</strong></p><p>Напряжение $U$.</p><p><strong>Решение:</strong></p><p>В рентгеновской трубке электроны ускоряются электрическим полем с напряжением $U$. При этом они приобретают кинетическую энергию $W_k$, которая равна работе электрического поля:</p><p>$W_k = eU$</p><p>где $e$ — это элементарный заряд.</p><p>При резком торможении электронов об анод трубки их кинетическая энергия превращается в энергию рентгеновских фотонов. Самое «жесткое» излучение (излучение с максимальной энергией и, следовательно, с минимальной длиной волны $\lambda_{min}$) возникает в том случае, когда вся кинетическая энергия одного электрона полностью переходит в энергию одного испущенного фотона.</p><p>Энергия фотона $E_{ф}$ определяется формулой Планка:</p><p>$E_{ф} = h\nu = \frac{hc}{\lambda}$</p><p>где $h$ — постоянная Планка, $\nu$ — частота излучения, $c$ — скорость света, $\lambda$ — длина волны.</p><p>Согласно закону сохранения энергии, приравниваем максимальную энергию фотона (соответствующую $\lambda_{min}$) к кинетической энергии электрона:</p><p>$E_{ф_{max}} = W_k$</p><p>$\frac{hc}{\lambda_{min}} = eU$</p><p>Из этого соотношения выразим искомое напряжение $U$:</p><p>$U = \frac{hc}{e\lambda_{min}}$</p><p>Подставим числовые значения в систему СИ:</p><p>$U = \frac{6,626 \cdot 10^{-34} \text{ Дж}\cdot\text{с} \cdot 3 \cdot 10^8 \text{ м/с}}{1,602 \cdot 10^{-19} \text{ Кл} \cdot 3,0 \cdot 10^{-11} \text{ м}} \approx \frac{19,878 \cdot 10^{-26}}{4,806 \cdot 10^{-30}} \text{ В}$</p><p>$U \approx 4,136 \cdot 10^4 \text{ В}$</p><p>Переведем результат в киловольты, зная, что 1 кВ = $10^3$ В:</p><p>$U \approx 41,36 \text{ кВ}$</p><p>Округляя до целых, получаем $U \approx 41$ кВ.</p><p><strong>Ответ:</strong> Напряжение, под которым работает рентгеновская трубка, составляет приблизительно $41$ кВ.</p>" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1319834" "type" => "task" ] "previous" => array:2 [ "refs" => "1319832" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1228 #items: array:1 [ 0 => App\Models\Book {#1048} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1341232" "type" => "book_page" ] ] #original: array:24 [ "id" => 1319833 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "271" "field_page_end" => null "field_url" => "/10-klass/fizika/gelfgat-zadachnik/39-1" "field_display_title" => "39.1" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1217} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1218} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1219} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1220} "content" => Illuminate\Database\Eloquent\Collection {#1222} "next" => array:2 [ "refs" => "1319834" "type" => "task" ] "previous" => array:2 [ "refs" => "1319832" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1228} "page" => array:2 [ "refs" => "1341232" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Task {#1223 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1319834 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "271" "field_page_end" => null "field_url" => "/10-klass/fizika/gelfgat-zadachnik/39-2" "field_display_title" => "39.2" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1221 #items: array:1 [ 0 => App\Models\Term {#1036} ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1230 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1226 #items: array:1 [ 0 => App\Models\Branch {#1120} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1224 #items: array:3 [ 0 => App\Models\Branch {#1120} 1 => App\Models\Branch {#1124} 2 => App\Models\Branch {#1128} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1227 #items: array:2 [ 0 => App\Models\Element {#1102} 1 => App\Models\Element {#1100} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1319835" "type" => "task" ] "previous" => array:2 [ "refs" => "1319833" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1225 #items: array:1 [ 0 => App\Models\Book {#1048} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1341232" "type" => "book_page" ] ] #original: array:24 [ "id" => 1319834 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "271" "field_page_end" => null "field_url" => "/10-klass/fizika/gelfgat-zadachnik/39-2" "field_display_title" => "39.2" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1221} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1230} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1226} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1224} "content" => Illuminate\Database\Eloquent\Collection {#1227} "next" => array:2 [ "refs" => "1319835" "type" => "task" ] "previous" => array:2 [ "refs" => "1319833" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1225} "page" => array:2 [ "refs" => "1341232" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Task {#1235 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1319835 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "271" "field_page_end" => null "field_url" => "/10-klass/fizika/gelfgat-zadachnik/39-3" "field_display_title" => "39.3" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1236 #items: array:1 [ 0 => App\Models\Term {#1036} ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1237 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1238 #items: array:1 [ 0 => App\Models\Branch {#1120} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1239 #items: array:3 [ 0 => App\Models\Branch {#1120} 1 => App\Models\Branch {#1124} 2 => App\Models\Branch {#1128} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1241 #items: array:2 [ 0 => App\Models\Element {#1250 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 1493970 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1251 #items: array:1 [ …1] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1319835" "type" => "task" ] "text" => "<p><strong>39.3.</strong> При освещении поверхности некоторого металла фиолетовым светом с длиной волны $\lambda_1 = 0,40$ мкм выбитые светом электроны задерживаются запирающим напряжением $U_1 = 2,0$ В. Чему равно запирающее напряжение $U_2$ при освещении того же металла красным светом с длиной волны $\lambda_2 = 0,77$ мкм?</p><p>☑ $ U_2 = 0,51$ В.</p><p><strong><em>Решение.</em></strong> Запирающее напряжение связано с максимальной кинетической энергией фотоэлектронов соотношением $W_k = eU$. Согласно уравнению Эйнштейна для фотоэффекта $hc/\lambda_1 = A + eU_1$, $hc/\lambda_2 = A + eU_2$. Отсюда</p><p>$U_2 = U_1 + \frac{hc}{e}\left(\frac{1}{\lambda_2} - \frac{1}{\lambda_1}\right) = 0,51$ (В).</p>" "img" => array:1 [ 0 => array:5 [ …5] ] ] #original: array:7 [ "id" => 1493970 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1251} "task" => array:2 [ "refs" => "1319835" "type" => "task" ] "text" => "<p><strong>39.3.</strong> При освещении поверхности некоторого металла фиолетовым светом с длиной волны $\lambda_1 = 0,40$ мкм выбитые светом электроны задерживаются запирающим напряжением $U_1 = 2,0$ В. Чему равно запирающее напряжение $U_2$ при освещении того же металла красным светом с длиной волны $\lambda_2 = 0,77$ мкм?</p><p>☑ $ U_2 = 0,51$ В.</p><p><strong><em>Решение.</em></strong> Запирающее напряжение связано с максимальной кинетической энергией фотоэлектронов соотношением $W_k = eU$. Согласно уравнению Эйнштейна для фотоэффекта $hc/\lambda_1 = A + eU_1$, $hc/\lambda_2 = A + eU_2$. Отсюда</p><p>$U_2 = U_1 + \frac{hc}{e}\left(\frac{1}{\lambda_2} - \frac{1}{\lambda_1}\right) = 0,51$ (В).</p>" "img" => array:1 [ 0 => array:5 [ …5] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Element {#1252 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1691527 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1253 #items: array:1 [ …1] #escapeWhenCastingToString: false } "task" => array:2 [ …2] "text" => "<p><strong>Дано:</strong></p><p>Длина волны фиолетового света, $λ_1 = 0,40$ мкм = $0,40 \times 10^{-6}$ м.</p><p>Запирающее напряжение для фиолетового света, $U_1 = 2,0$ В.</p><p>Длина волны красного света, $λ_2 = 0,77$ мкм = $0,77 \times 10^{-6}$ м.</p><p>Постоянная Планка, $h \approx 6,63 \times 10^{-34}$ Дж·с.</p><p>Скорость света в вакууме, $c \approx 3 \times 10^8$ м/с.</p><p>Элементарный заряд, $e \approx 1,6 \times 10^{-19}$ Кл.</p><p><strong>Найти:</strong></p><p>$U_2$ — запирающее напряжение для красного света.</p><p><strong>Решение:</strong></p><p>Для решения задачи воспользуемся уравнением Эйнштейна для фотоэффекта, которое связывает энергию падающего фотона $E_{ф}$, работу выхода электрона из металла $A$ и максимальную кинетическую энергию фотоэлектрона $W_k$:</p><p>$E_{ф} = A + W_k$</p><p>Энергия фотона определяется его частотой $ν$ или длиной волны $λ$ как $E_{ф} = hν = \frac{hc}{λ}$.</p><p>Максимальная кинетическая энергия фотоэлектронов связана с запирающим (задерживающим) напряжением $U$ соотношением $W_k = eU$.</p><p>Таким образом, уравнение Эйнштейна можно записать в виде: $\frac{hc}{λ} = A + eU$.</p><p>Составим систему из двух уравнений для двух случаев, описанных в задаче:</p><p><strong>1.</strong> Для фиолетового света ($λ_1$, $U_1$):</p><p>$\frac{hc}{λ_1} = A + eU_1$</p><p><strong>2.</strong> Для красного света ($λ_2$, $U_2$):</p><p>$\frac{hc}{λ_2} = A + eU_2$</p><p>Работа выхода $A$ зависит только от материала поверхности и в обоих случаях одинакова. Выразим работу выхода из первого уравнения:</p><p>$A = \frac{hc}{λ_1} - eU_1$</p><p>Теперь подставим это выражение во второе уравнение:</p><p>$\frac{hc}{λ_2} = (\frac{hc}{λ_1} - eU_1) + eU_2$</p><p>Выразим из полученного уравнения искомую величину $eU_2$:</p><p>$eU_2 = \frac{hc}{λ_2} - \frac{hc}{λ_1} + eU_1$</p><p>Разделим обе части на заряд электрона $e$, чтобы найти $U_2$:</p><p>$U_2 = \frac{hc}{eλ_2} - \frac{hc}{eλ_1} + U_1$</p><p>Сгруппируем слагаемые для удобства вычислений:</p><p>$U_2 = U_1 + \frac{hc}{e} \left( \frac{1}{λ_2} - \frac{1}{λ_1} \right)$</p><p>Перед вычислением убедимся, что при освещении красным светом фотоэффект вообще возможен. Для этого энергия фотона красного света $E_{ф2}$ должна быть больше работы выхода $A$.</p><p>Найдем работу выхода из первого случая:</p><p>$A = \frac{6,63 \times 10^{-34} \text{ Дж·с} \times 3 \times 10^8 \text{ м/с}}{0,40 \times 10^{-6} \text{ м}} - 1,6 \times 10^{-19} \text{ Кл} \times 2,0 \text{ В} \approx 4,97 \times 10^{-19} \text{ Дж} - 3,2 \times 10^{-19} \text{ Дж} = 1,77 \times 10^{-19} \text{ Дж}$</p><p>Найдем энергию фотона красного света:</p><p>$E_{ф2} = \frac{hc}{λ_2} = \frac{6,63 \times 10^{-34} \text{ Дж·с} \times 3 \times 10^8 \text{ м/с}}{0,77 \times 10^{-6} \text{ м}} \approx 2,58 \times 10^{-19} \text{ Дж}$</p><p>Поскольку $E_{ф2} > A$ ($2,58 \times 10^{-19} \text{ Дж} > 1,77 \times 10^{-19} \text{ Дж}$), фотоэффект будет наблюдаться.</p><p>Подставим числовые значения в выведенную формулу для $U_2$:</p><p>$U_2 = 2,0 \text{ В} + \frac{6,63 \times 10^{-34} \text{ Дж·с} \times 3 \times 10^8 \text{ м/с}}{1,6 \times 10^{-19} \text{ Кл}} \left( \frac{1}{0,77 \times 10^{-6} \text{ м}} - \frac{1}{0,40 \times 10^{-6} \text{ м}} \right)$</p><p>$U_2 = 2,0 + 1,243 \times 10^{-6} \left( \frac{1}{10^{-6}} \left( \frac{1}{0,77} - \frac{1}{0,40} \right) \right)$</p><p>$U_2 = 2,0 + 1,243 \left( \frac{0,40 - 0,77}{0,77 \times 0,40} \right)$</p><p>$U_2 = 2,0 + 1,243 \left( \frac{-0,37}{0,308} \right)$</p><p>$U_2 = 2,0 + 1,243 \times (-1,2013)$</p><p>$U_2 = 2,0 - 1,493 \approx 0,507 \text{ В}$</p><p>Округляя результат до двух значащих цифр, получаем $0,51$ В.</p><p><strong>Ответ:</strong> $U_2 = 0,51$ В.</p>" ] #original: array:6 [ "id" => 1691527 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1253} "task" => array:2 [ …2] "text" => "<p><strong>Дано:</strong></p><p>Длина волны фиолетового света, $λ_1 = 0,40$ мкм = $0,40 \times 10^{-6}$ м.</p><p>Запирающее напряжение для фиолетового света, $U_1 = 2,0$ В.</p><p>Длина волны красного света, $λ_2 = 0,77$ мкм = $0,77 \times 10^{-6}$ м.</p><p>Постоянная Планка, $h \approx 6,63 \times 10^{-34}$ Дж·с.</p><p>Скорость света в вакууме, $c \approx 3 \times 10^8$ м/с.</p><p>Элементарный заряд, $e \approx 1,6 \times 10^{-19}$ Кл.</p><p><strong>Найти:</strong></p><p>$U_2$ — запирающее напряжение для красного света.</p><p><strong>Решение:</strong></p><p>Для решения задачи воспользуемся уравнением Эйнштейна для фотоэффекта, которое связывает энергию падающего фотона $E_{ф}$, работу выхода электрона из металла $A$ и максимальную кинетическую энергию фотоэлектрона $W_k$:</p><p>$E_{ф} = A + W_k$</p><p>Энергия фотона определяется его частотой $ν$ или длиной волны $λ$ как $E_{ф} = hν = \frac{hc}{λ}$.</p><p>Максимальная кинетическая энергия фотоэлектронов связана с запирающим (задерживающим) напряжением $U$ соотношением $W_k = eU$.</p><p>Таким образом, уравнение Эйнштейна можно записать в виде: $\frac{hc}{λ} = A + eU$.</p><p>Составим систему из двух уравнений для двух случаев, описанных в задаче:</p><p><strong>1.</strong> Для фиолетового света ($λ_1$, $U_1$):</p><p>$\frac{hc}{λ_1} = A + eU_1$</p><p><strong>2.</strong> Для красного света ($λ_2$, $U_2$):</p><p>$\frac{hc}{λ_2} = A + eU_2$</p><p>Работа выхода $A$ зависит только от материала поверхности и в обоих случаях одинакова. Выразим работу выхода из первого уравнения:</p><p>$A = \frac{hc}{λ_1} - eU_1$</p><p>Теперь подставим это выражение во второе уравнение:</p><p>$\frac{hc}{λ_2} = (\frac{hc}{λ_1} - eU_1) + eU_2$</p><p>Выразим из полученного уравнения искомую величину $eU_2$:</p><p>$eU_2 = \frac{hc}{λ_2} - \frac{hc}{λ_1} + eU_1$</p><p>Разделим обе части на заряд электрона $e$, чтобы найти $U_2$:</p><p>$U_2 = \frac{hc}{eλ_2} - \frac{hc}{eλ_1} + U_1$</p><p>Сгруппируем слагаемые для удобства вычислений:</p><p>$U_2 = U_1 + \frac{hc}{e} \left( \frac{1}{λ_2} - \frac{1}{λ_1} \right)$</p><p>Перед вычислением убедимся, что при освещении красным светом фотоэффект вообще возможен. Для этого энергия фотона красного света $E_{ф2}$ должна быть больше работы выхода $A$.</p><p>Найдем работу выхода из первого случая:</p><p>$A = \frac{6,63 \times 10^{-34} \text{ Дж·с} \times 3 \times 10^8 \text{ м/с}}{0,40 \times 10^{-6} \text{ м}} - 1,6 \times 10^{-19} \text{ Кл} \times 2,0 \text{ В} \approx 4,97 \times 10^{-19} \text{ Дж} - 3,2 \times 10^{-19} \text{ Дж} = 1,77 \times 10^{-19} \text{ Дж}$</p><p>Найдем энергию фотона красного света:</p><p>$E_{ф2} = \frac{hc}{λ_2} = \frac{6,63 \times 10^{-34} \text{ Дж·с} \times 3 \times 10^8 \text{ м/с}}{0,77 \times 10^{-6} \text{ м}} \approx 2,58 \times 10^{-19} \text{ Дж}$</p><p>Поскольку $E_{ф2} > A$ ($2,58 \times 10^{-19} \text{ Дж} > 1,77 \times 10^{-19} \text{ Дж}$), фотоэффект будет наблюдаться.</p><p>Подставим числовые значения в выведенную формулу для $U_2$:</p><p>$U_2 = 2,0 \text{ В} + \frac{6,63 \times 10^{-34} \text{ Дж·с} \times 3 \times 10^8 \text{ м/с}}{1,6 \times 10^{-19} \text{ Кл}} \left( \frac{1}{0,77 \times 10^{-6} \text{ м}} - \frac{1}{0,40 \times 10^{-6} \text{ м}} \right)$</p><p>$U_2 = 2,0 + 1,243 \times 10^{-6} \left( \frac{1}{10^{-6}} \left( \frac{1}{0,77} - \frac{1}{0,40} \right) \right)$</p><p>$U_2 = 2,0 + 1,243 \left( \frac{0,40 - 0,77}{0,77 \times 0,40} \right)$</p><p>$U_2 = 2,0 + 1,243 \left( \frac{-0,37}{0,308} \right)$</p><p>$U_2 = 2,0 + 1,243 \times (-1,2013)$</p><p>$U_2 = 2,0 - 1,493 \approx 0,507 \text{ В}$</p><p>Округляя результат до двух значащих цифр, получаем $0,51$ В.</p><p><strong>Ответ:</strong> $U_2 = 0,51$ В.</p>" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1319836" "type" => "task" ] "previous" => array:2 [ "refs" => "1319834" "type" => "task" ] "book" => 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№39.2 (с. 271)
Условие. №39.2 (с. 271)
скриншот условия
39.2. Для калия красная граница фотоэффекта равна $\lambda_{max} = 0,62 \text{ мкм}$. Какую максимальную скорость $\upsilon$ могут иметь фотоэлектроны, вылетающие при облучении калия фиолетовым светом с длиной волны $\lambda = 0,42 \text{ мкм}$?
☑ $\upsilon = 580 \text{ км/с}$.
Решение. Работа выхода совпадает с минимальной энергией фотона, вызывающего фотоэффект: $A = hc/\lambda_{max}$. Тогда из уравнения Эйнштейна для фотоэффекта следует:
$\upsilon = \sqrt{\frac{2hc(\lambda_{max} - \lambda)}{m\lambda\lambda_{max}}} = 5,8 \cdot 10^5 \text{ (м/с)}$.
Решение. №39.2 (с. 271)
Дано:
Красная граница фотоэффекта для калия, $ \lambda_{max} = 0,62 \text{ мкм} = 0,62 \cdot 10^{-6} \text{ м} $
Длина волны падающего фиолетового света, $ \lambda = 0,42 \text{ мкм} = 0,42 \cdot 10^{-6} \text{ м} $
Постоянная Планка, $ h \approx 6,63 \cdot 10^{-34} \text{ Дж} \cdot \text{с} $
Скорость света в вакууме, $ c \approx 3 \cdot 10^8 \text{ м/с} $
Масса электрона, $ m_e \approx 9,11 \cdot 10^{-31} \text{ кг} $
Найти:
Максимальную скорость фотоэлектронов $ v $.
Решение:
Для решения задачи используется уравнение Эйнштейна для фотоэффекта, которое связывает энергию падающего фотона, работу выхода электрона из металла и максимальную кинетическую энергию вылетевшего электрона:
$ E_{photon} = A_{вых} + E_{k, max} $
Энергия падающего фотона ($ E_{photon} $) определяется его длиной волны $ \lambda $ по формуле:
$ E_{photon} = \frac{hc}{\lambda} $
Работа выхода ($ A_{вых} $) — это минимальная энергия, которую нужно сообщить электрону, чтобы он покинул металл. Эта энергия соответствует энергии фотона с длиной волны, равной красной границе фотоэффекта ($ \lambda_{max} $):
$ A_{вых} = \frac{hc}{\lambda_{max}} $
Максимальная кинетическая энергия ($ E_{k, max} $) фотоэлектрона связана с его максимальной скоростью $ v $ соотношением:
$ E_{k, max} = \frac{m_e v^2}{2} $
Подставим все эти выражения в исходное уравнение Эйнштейна:
$ \frac{hc}{\lambda} = \frac{hc}{\lambda_{max}} + \frac{m_e v^2}{2} $
Выразим из этого уравнения член, содержащий кинетическую энергию:
$ \frac{m_e v^2}{2} = \frac{hc}{\lambda} - \frac{hc}{\lambda_{max}} $
Вынесем общий множитель $ hc $ за скобки и приведем дроби в скобках к общему знаменателю:
$ \frac{m_e v^2}{2} = hc \left( \frac{1}{\lambda} - \frac{1}{\lambda_{max}} \right) = hc \frac{\lambda_{max} - \lambda}{\lambda \lambda_{max}} $
Теперь выразим квадрат максимальной скорости $ v^2 $:
$ v^2 = \frac{2hc(\lambda_{max} - \lambda)}{m_e \lambda \lambda_{max}} $
Осталось извлечь квадратный корень, чтобы найти искомую скорость $ v $:
$ v = \sqrt{\frac{2hc(\lambda_{max} - \lambda)}{m_e \lambda \lambda_{max}}} $
Подставим числовые значения в полученную формулу:
$ v = \sqrt{\frac{2 \cdot (6,63 \cdot 10^{-34} \text{ Дж} \cdot \text{с}) \cdot (3 \cdot 10^8 \text{ м/с}) \cdot (0,62 \cdot 10^{-6} \text{ м} - 0,42 \cdot 10^{-6} \text{ м})}{(9,11 \cdot 10^{-31} \text{ кг}) \cdot (0,42 \cdot 10^{-6} \text{ м}) \cdot (0,62 \cdot 10^{-6} \text{ м})}} $
$ v = \sqrt{\frac{2 \cdot 6,63 \cdot 3 \cdot 10^{-26} \cdot (0,20 \cdot 10^{-6})}{9,11 \cdot 0,42 \cdot 0,62 \cdot 10^{-43}}} = \sqrt{\frac{7,956 \cdot 10^{-32}}{2,374 \cdot 10^{-43}}} $
$ v \approx \sqrt{3,351 \cdot 10^{11}} \text{ м/с} \approx 5,789 \cdot 10^5 \text{ м/с} $
Округлим результат до двух значащих цифр и переведем в километры в секунду ($ 1 \text{ км/с} = 1000 \text{ м/с} $):
$ v \approx 5,8 \cdot 10^5 \text{ м/с} = 580 \cdot 10^3 \text{ м/с} = 580 \text{ км/с} $
Ответ: $ v \approx 580 \text{ км/с} $
Другие задания:
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ПрисоединитьсяМы подготовили для вас ответ c подробным объяснением домашего задания по физике за 10-11 класс, для упражнения номер 39.2 расположенного на странице 271 к задачнику 2008 года издания для учащихся школ и гимназий.
Теперь на нашем сайте ГДЗ.ТОП вы всегда легко и бесплатно найдёте условие с правильным ответом на вопрос «Как решить ДЗ» и «Как сделать» задание по физике к упражнению №39.2 (с. 271), авторов: Гельфгат (Илья Маркович), Генденштейн (Лев Элевич), Кирик (Леонид Анатольевич), профильный уровень обучения учебного пособия издательства Илекса.