gdz.top
Номер 30.7, страница 217 - 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
Электродинамика. Постоянный электрический ток. 30. Электрический ток в металлах, жидкостях, газах и вакууме. Полупроводники. Упражнения - номер 30.7, страница 217.
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" => 1319742 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "217" "field_page_end" => null "field_url" => "/10-klass/fizika/gelfgat-zadachnik/30-7" "field_display_title" => "30.7" "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" => 1319339 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Электродинамика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1047 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "163" "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 {#1057 #items: array:1 [ 0 => App\Models\Book {#1056 #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 {#1061 #items: array:1 [ 0 => 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: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 {#1063 #items: array:2 [ 0 => App\Models\Term {#1071 #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 {#1072 #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 {#1062 #items: array:1 [ 0 => App\Models\Term {#1068 #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 {#1070 #items: array:3 [ 0 => App\Models\Term {#1077 #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 {#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: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 {#1079 #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 {#1074 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1075 #items: array:1 [ 0 => App\Models\Term {#1060 #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 {#1066 #items: array:1 [ 0 => App\Models\Term {#1073 #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 {#1064 #items: array:1 [ 0 => App\Models\Term {#1067 #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 {#1065 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1059 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1089 #items: array:1 [ 0 => App\Models\Term {#1088 #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 {#1081 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1082 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1080 #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 {#1085 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1083 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1086 #items: [] #escapeWhenCastingToString: false } "field_url" => "/10-klass/fizika/gelfgat-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1098 #items: array:1 [ 0 => App\Models\Term {#1097 #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 {#1061} "field_class" => Illuminate\Database\Eloquent\Collection {#1063} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1062} "field_author" => Illuminate\Database\Eloquent\Collection {#1070} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1074} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1075} "field_country" => Illuminate\Database\Eloquent\Collection {#1066} "field_city" => Illuminate\Database\Eloquent\Collection {#1064} "field_series" => Illuminate\Database\Eloquent\Collection {#1065} "field_umk" => Illuminate\Database\Eloquent\Collection {#1059} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1089} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1081} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1082} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1080} "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 {#1085} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1083} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1086} "field_url" => "/10-klass/fizika/gelfgat-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1098} "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 {#1049 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1319339 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Электродинамика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1047} "field_page_start" => "163" "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 {#1057} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1049} ] #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 {#1116 #items: array:4 [ 0 => App\Models\Branch {#1126 #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" => 1319339 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Электродинамика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1127 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "163" "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 {#1128 #items: array:1 [ 0 => App\Models\Book {#1056} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1129 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1319339 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Электродинамика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1127} "field_page_start" => "163" "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 {#1128} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1129} ] #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 {#1130 #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" => 1319350 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Постоянный электрический ток" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1131 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "188" "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 {#1132 #items: array:1 [ 0 => App\Models\Book {#1056} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1133 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1319350 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Постоянный электрический ток" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1131} "field_page_start" => "188" "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 {#1132} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1133} ] #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 {#1134 #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" => 1319361 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "30. Электрический ток в металлах, жидкостях, газах и вакууме. Полупроводники" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1135 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "215" "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 {#1136 #items: array:1 [ 0 => App\Models\Book {#1056} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1145 #items: array:1 [ 0 => App\Models\Branch {#1144 #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" => 1319350 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Постоянный электрический ток" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1146 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "188" "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 {#1147 #items: array:1 [ 0 => App\Models\Book {#1056} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1148 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1319350 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Постоянный электрический ток" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1146} "field_page_start" => "188" "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 {#1147} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1148} ] #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" => 1319361 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "30. Электрический ток в металлах, жидкостях, газах и вакууме. Полупроводники" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1135} "field_page_start" => "215" "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 {#1136} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1145} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 3 => 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" => 1319362 "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 {#1137 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "215" "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 {#1056} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1154 #items: array:1 [ 0 => App\Models\Branch {#1153 #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" => 1319361 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "30. Электрический ток в металлах, жидкостях, газах и вакууме. Полупроводники" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1155 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "215" "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 {#1156 #items: array:1 [ 0 => App\Models\Book {#1056} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1157 #items: array:1 [ 0 => App\Models\Branch {#1144} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1319361 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "30. Электрический ток в металлах, жидкостях, газах и вакууме. Полупроводники" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1155} "field_page_start" => "215" "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 {#1156} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1157} ] #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" => 1319362 "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 {#1137} "field_page_start" => "215" "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 {#1154} ] #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 {#1107 #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" => 1493905 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1095 #items: array:1 [ 0 => App\Models\Edition {#1106 #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 {#1103 #items: array:1 [ 0 => App\Models\Term {#1105 #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 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #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 {#1104 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1102 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1101 #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 {#1103} "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 {#1104} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1102} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1101} "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" => "1319742" "type" => "task" ] "text" => "<p><strong>30.7.</strong> Какой наименьшей кинетической энергией $W_k$ и скоростью $\text{v}$ должен обладать ион неона, чтобы при столкновении его с неподвижным нейтральным атомом неона могла произойти ионизация атома? Потенциал ионизации атомов неона $\varphi = 21,5$ В.</p><p>☑ $W_k = 43 \text{ эВ} = 6,9 \cdot 10^{8} \text{ Дж}$; 20 км/с.</p><p><strong><em>Решение.</em></strong> Поскольку массы сталкивающихся частиц практически одинаковы, следует учесть кинетическую энергию, которую имеют частицы после столкновения. Наиболее эффективным для ионизации является неупругий удар, после которого обе частицы имеют одинаковую скорость, равную половине начальной скорости иона $v_0$. Суммарная кинетическая энергия частиц после неупругого удара $2 \cdot \frac{m_0 (v_0/2)^2}{2} = \frac{W_k}{2}$. Здесь $m_0 = M/N_A$ ($\text{M}$ — молярная масса неона). Согласно закону сохранения энергии: $W_k = e\varphi + W_k/2$.</p><p>Отсюда $W_k = 2e\varphi = 43 \text{ (эВ)} = 6,9 \cdot 10^{8} \text{ (Дж)}$ и $v = 2\sqrt{\frac{eN_A\varphi}{M}} = 2,0 \cdot 10^4 \text{ (м/с)}$.</p><p>Таким образом, для ионизации одного и того же атома ион должен иметь вдвое большую энергию, чем электрон.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "7-1.jpg" "alt" => null "width" => "1380" "height" => 1301 "path" => "/media/fizika_10/gelfgat-z/0-30/7-1.webp?ts=1756251127" ] ] ] #original: array:7 [ "id" => 1493905 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1095} "task" => array:2 [ "refs" => "1319742" "type" => "task" ] "text" => "<p><strong>30.7.</strong> Какой наименьшей кинетической энергией $W_k$ и скоростью $\text{v}$ должен обладать ион неона, чтобы при столкновении его с неподвижным нейтральным атомом неона могла произойти ионизация атома? Потенциал ионизации атомов неона $\varphi = 21,5$ В.</p><p>☑ $W_k = 43 \text{ эВ} = 6,9 \cdot 10^{8} \text{ Дж}$; 20 км/с.</p><p><strong><em>Решение.</em></strong> Поскольку массы сталкивающихся частиц практически одинаковы, следует учесть кинетическую энергию, которую имеют частицы после столкновения. Наиболее эффективным для ионизации является неупругий удар, после которого обе частицы имеют одинаковую скорость, равную половине начальной скорости иона $v_0$. Суммарная кинетическая энергия частиц после неупругого удара $2 \cdot \frac{m_0 (v_0/2)^2}{2} = \frac{W_k}{2}$. Здесь $m_0 = M/N_A$ ($\text{M}$ — молярная масса неона). Согласно закону сохранения энергии: $W_k = e\varphi + W_k/2$.</p><p>Отсюда $W_k = 2e\varphi = 43 \text{ (эВ)} = 6,9 \cdot 10^{8} \text{ (Дж)}$ и $v = 2\sqrt{\frac{eN_A\varphi}{M}} = 2,0 \cdot 10^4 \text{ (м/с)}$.</p><p>Таким образом, для ионизации одного и того же атома ион должен иметь вдвое большую энергию, чем электрон.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "7-1.jpg" "alt" => null "width" => "1380" "height" => 1301 "path" => "/media/fizika_10/gelfgat-z/0-30/7-1.webp?ts=1756251127" ] ] ] #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 {#1099 #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" => 1691462 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1052 #items: array:1 [ 0 => App\Models\Edition {#1100 #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 {#1094 #items: array:1 [ 0 => App\Models\Term {#1093 #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 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #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 {#1092 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1084 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1054 #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 {#1094} "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 {#1092} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1084} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1054} "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" => "1319742" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Потенциал ионизации атомов неона: $\phi = 21,5 \text{ В}$</p><p>Элементарный заряд: $e \approx 1,6 \cdot 10^{-19} \text{ Кл}$</p><p>Молярная масса неона: $M \approx 20,18 \cdot 10^{-3} \text{ кг/моль}$</p><p>Число Авогадро: $N_A \approx 6,022 \cdot 10^{23} \text{ моль}^{-1}$</p><p>Масса иона неона $m_1$ и масса атома неона $m_2$ приблизительно равны: $m_1 \approx m_2 = m$</p><p><strong>Найти:</strong></p><p>Наименьшая кинетическая энергия иона: $W_k$</p><p>Наименьшая скорость иона: $v$</p><p><strong>Решение:</strong></p><p>Для того чтобы произошла ионизация, часть кинетической энергии налетающего иона должна перейти во внутреннюю энергию атома, достаточную для отрыва электрона. Минимальная необходимая для этого энергия — это энергия ионизации $W_{ион} = e\phi$.</p><p>Вопрос стоит о наименьшей начальной энергии иона, при которой ионизация возможна. Это соответствует ситуации, когда максимальная доля начальной кинетической энергии переходит во внутреннюю. Такой процесс происходит при абсолютно неупругом ударе, когда после столкновения обе частицы (ион и атом) движутся вместе с одинаковой скоростью $u$.</p><p>Так как сталкиваются ион неона и нейтральный атом неона, их массы можно считать одинаковыми: $m_1 = m_2 = m$.</p><p>Запишем закон сохранения импульса для системы "ион-атом". Начальный импульс системы равен импульсу налетающего иона (так как атом покоится), а конечный импульс — это импульс двух слипшихся частиц.</p><p>$m v = (m + m) u$</p><p>$m v = 2m u$</p><p>Отсюда находим скорость частиц после столкновения:</p><p>$u = \frac{v}{2}$</p><p>Теперь запишем закон сохранения энергии. Начальная энергия системы — это кинетическая энергия иона $W_k$. После столкновения эта энергия перераспределяется между суммарной кинетической энергией двух частиц $W_{k'}$ и энергией, пошедшей на ионизацию атома $W_{ион}$.</p><p>$W_k = W_{k'} + W_{ион}$</p><p>Начальная кинетическая энергия иона:</p><p>$W_k = \frac{m v^2}{2}$</p><p>Конечная кинетическая энергия системы:</p><p>$W_{k'} = \frac{(m+m)u^2}{2} = \frac{2m(\frac{v}{2})^2}{2} = \frac{2m \frac{v^2}{4}}{2} = \frac{m v^2}{4}$</p><p>Сравнивая выражения для $W_k$ и $W_{k'}$, видим, что $W_{k'} = \frac{W_k}{2}$. Это означает, что при абсолютно неупругом столкновении двух тел равной массы половина начальной кинетической энергии переходит в кинетическую энергию системы после удара, а вторая половина может быть преобразована во внутреннюю энергию.</p><p>Подставим это в закон сохранения энергии:</p><p>$W_k = \frac{W_k}{2} + W_{ион}$</p><p>Отсюда минимальная энергия, необходимая для ионизации, равна:</p><p>$\frac{W_k}{2} = W_{ион} = e\phi$</p><p>$W_k = 2 e \phi$</p><p>Таким образом, наименьшая кинетическая энергия налетающего иона должна быть вдвое больше энергии ионизации атома.</p><p>Вычислим значение $W_k$ в электрон-вольтах (эВ) и в джоулях (Дж):</p><p>$W_k = 2 \cdot 21,5 \text{ эВ} = 43 \text{ эВ}$</p><p>$W_k = 2 \cdot (1,6 \cdot 10^{-19} \text{ Кл}) \cdot 21,5 \text{ В} = 6,88 \cdot 10^{-18} \text{ Дж} \approx 6,9 \cdot 10^{-18} \text{ Дж}$</p><p>Теперь найдем начальную скорость иона $v$ из формулы кинетической энергии $W_k = \frac{m v^2}{2}$.</p><p>$v = \sqrt{\frac{2 W_k}{m}}$</p><p>Массу атома неона $m$ найдем через молярную массу $M$ и число Авогадро $N_A$:</p><p>$m = \frac{M}{N_A} = \frac{20,18 \cdot 10^{-3} \text{ кг/моль}}{6,022 \cdot 10^{23} \text{ моль}^{-1}} \approx 3,35 \cdot 10^{-26} \text{ кг}$</p><p>Подставим значения и вычислим скорость:</p><p>$v = \sqrt{\frac{2 \cdot 6,9 \cdot 10^{-18} \text{ Дж}}{3,35 \cdot 10^{-26} \text{ кг}}} \approx \sqrt{4,12 \cdot 10^8 \frac{\text{м}^2}{\text{с}^2}} \approx 2,03 \cdot 10^4 \text{ м/с}$</p><p>Округлим результат:</p><p>$v \approx 2,0 \cdot 10^4 \text{ м/с} = 20 \text{ км/с}$</p><p><strong>Ответ:</strong> $W_k = 43 \text{ эВ} \approx 6,9 \cdot 10^{-18} \text{ Дж}$; $v \approx 2,0 \cdot 10^4 \text{ м/с} = 20 \text{ км/с}$.</p>" ] #original: array:6 [ "id" => 1691462 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1052} "task" => array:2 [ "refs" => "1319742" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Потенциал ионизации атомов неона: $\phi = 21,5 \text{ В}$</p><p>Элементарный заряд: $e \approx 1,6 \cdot 10^{-19} \text{ Кл}$</p><p>Молярная масса неона: $M \approx 20,18 \cdot 10^{-3} \text{ кг/моль}$</p><p>Число Авогадро: $N_A \approx 6,022 \cdot 10^{23} \text{ моль}^{-1}$</p><p>Масса иона неона $m_1$ и масса атома неона $m_2$ приблизительно равны: $m_1 \approx m_2 = m$</p><p><strong>Найти:</strong></p><p>Наименьшая кинетическая энергия иона: $W_k$</p><p>Наименьшая скорость иона: $v$</p><p><strong>Решение:</strong></p><p>Для того чтобы произошла ионизация, часть кинетической энергии налетающего иона должна перейти во внутреннюю энергию атома, достаточную для отрыва электрона. Минимальная необходимая для этого энергия — это энергия ионизации $W_{ион} = e\phi$.</p><p>Вопрос стоит о наименьшей начальной энергии иона, при которой ионизация возможна. Это соответствует ситуации, когда максимальная доля начальной кинетической энергии переходит во внутреннюю. Такой процесс происходит при абсолютно неупругом ударе, когда после столкновения обе частицы (ион и атом) движутся вместе с одинаковой скоростью $u$.</p><p>Так как сталкиваются ион неона и нейтральный атом неона, их массы можно считать одинаковыми: $m_1 = m_2 = m$.</p><p>Запишем закон сохранения импульса для системы "ион-атом". Начальный импульс системы равен импульсу налетающего иона (так как атом покоится), а конечный импульс — это импульс двух слипшихся частиц.</p><p>$m v = (m + m) u$</p><p>$m v = 2m u$</p><p>Отсюда находим скорость частиц после столкновения:</p><p>$u = \frac{v}{2}$</p><p>Теперь запишем закон сохранения энергии. Начальная энергия системы — это кинетическая энергия иона $W_k$. После столкновения эта энергия перераспределяется между суммарной кинетической энергией двух частиц $W_{k'}$ и энергией, пошедшей на ионизацию атома $W_{ион}$.</p><p>$W_k = W_{k'} + W_{ион}$</p><p>Начальная кинетическая энергия иона:</p><p>$W_k = \frac{m v^2}{2}$</p><p>Конечная кинетическая энергия системы:</p><p>$W_{k'} = \frac{(m+m)u^2}{2} = \frac{2m(\frac{v}{2})^2}{2} = \frac{2m \frac{v^2}{4}}{2} = \frac{m v^2}{4}$</p><p>Сравнивая выражения для $W_k$ и $W_{k'}$, видим, что $W_{k'} = \frac{W_k}{2}$. Это означает, что при абсолютно неупругом столкновении двух тел равной массы половина начальной кинетической энергии переходит в кинетическую энергию системы после удара, а вторая половина может быть преобразована во внутреннюю энергию.</p><p>Подставим это в закон сохранения энергии:</p><p>$W_k = \frac{W_k}{2} + W_{ион}$</p><p>Отсюда минимальная энергия, необходимая для ионизации, равна:</p><p>$\frac{W_k}{2} = W_{ион} = e\phi$</p><p>$W_k = 2 e \phi$</p><p>Таким образом, наименьшая кинетическая энергия налетающего иона должна быть вдвое больше энергии ионизации атома.</p><p>Вычислим значение $W_k$ в электрон-вольтах (эВ) и в джоулях (Дж):</p><p>$W_k = 2 \cdot 21,5 \text{ эВ} = 43 \text{ эВ}$</p><p>$W_k = 2 \cdot (1,6 \cdot 10^{-19} \text{ Кл}) \cdot 21,5 \text{ В} = 6,88 \cdot 10^{-18} \text{ Дж} \approx 6,9 \cdot 10^{-18} \text{ Дж}$</p><p>Теперь найдем начальную скорость иона $v$ из формулы кинетической энергии $W_k = \frac{m v^2}{2}$.</p><p>$v = \sqrt{\frac{2 W_k}{m}}$</p><p>Массу атома неона $m$ найдем через молярную массу $M$ и число Авогадро $N_A$:</p><p>$m = \frac{M}{N_A} = \frac{20,18 \cdot 10^{-3} \text{ кг/моль}}{6,022 \cdot 10^{23} \text{ моль}^{-1}} \approx 3,35 \cdot 10^{-26} \text{ кг}$</p><p>Подставим значения и вычислим скорость:</p><p>$v = \sqrt{\frac{2 \cdot 6,9 \cdot 10^{-18} \text{ Дж}}{3,35 \cdot 10^{-26} \text{ кг}}} \approx \sqrt{4,12 \cdot 10^8 \frac{\text{м}^2}{\text{с}^2}} \approx 2,03 \cdot 10^4 \text{ м/с}$</p><p>Округлим результат:</p><p>$v \approx 2,0 \cdot 10^4 \text{ м/с} = 20 \text{ км/с}$</p><p><strong>Ответ:</strong> $W_k = 43 \text{ эВ} \approx 6,9 \cdot 10^{-18} \text{ Дж}$; $v \approx 2,0 \cdot 10^4 \text{ м/с} = 20 \text{ км/с}$.</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" => "1319743" "type" => "task" ] "previous" => array:2 [ "refs" => "1319741" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1110 #items: array:1 [ 0 => App\Models\Book {#1056} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1042 #items: array:1 [ 0 => App\Models\BookPage {#1112 #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" => 1341178 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "217" "field_url" => "/10-klass/fizika/gelfgat-zadachnik/page-217" "field_display_title" => "217" "field_folder" => "1" "field_image_name" => "217" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1091 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1090 #items: array:1 [ 0 => App\Models\Book {#1056} ] #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 {#1053 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1122 #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" => 1519723 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1121 #items: array:1 [ 0 => App\Models\Edition {#1106} ] #escapeWhenCastingToString: false } "book_page" => array:2 [ "refs" => "1341178" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "217-1.jpg" "alt" => null "width" => "1550" "height" => 2448 "path" => "/media/fizika_10/gelfgat-z/0-1/217-1.webp?ts=1756642390" ] ] ] #original: array:6 [ "id" => 1519723 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1121} "book_page" => array:2 [ "refs" => "1341178" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "217-1.jpg" "alt" => null "width" => "1550" "height" => 2448 "path" => "/media/fizika_10/gelfgat-z/0-1/217-1.webp?ts=1756642390" ] ] ] #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" => "1341179" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1341177" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1224 #items: array:3 [ 0 => App\Models\Task {#1234 #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" => 1319741 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "216" "field_page_end" => "217" "field_url" => "/10-klass/fizika/gelfgat-zadachnik/30-6" "field_display_title" => "30.6" "field_outside_task" => "0" "field_task_type" => Illuminate\Database\Eloquent\Collection {#1235 #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 {#1236 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1237 #items: array:1 [ 0 => App\Models\Branch {#1126} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1238 #items: array:4 [ 0 => App\Models\Branch {#1126} 1 => App\Models\Branch {#1130} 2 => App\Models\Branch {#1134} 3 => App\Models\Branch {#1138} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1240 #items: array:2 [ 0 => App\Models\Element {#1249 #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 [ …7] #original: array:7 [ …7] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 1 => App\Models\Element {#1251 #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 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1319742" "type" => "task" ] "previous" => array:2 [ "refs" => "1319740" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1246 #items: array:1 [ 0 => App\Models\Book {#1056} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1341177" "type" => "book_page" ] ] #original: array:24 [ "id" => 1319741 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "216" "field_page_end" => "217" "field_url" => "/10-klass/fizika/gelfgat-zadachnik/30-6" "field_display_title" => "30.6" "field_outside_task" => "0" "field_task_type" => Illuminate\Database\Eloquent\Collection {#1235} "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 {#1236} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1237} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1238} "content" => Illuminate\Database\Eloquent\Collection {#1240} "next" => array:2 [ "refs" => "1319742" "type" => "task" ] "previous" => array:2 [ "refs" => "1319740" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1246} "page" => array:2 [ "refs" => "1341177" "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 {#1241 #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" => 1319742 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "217" "field_page_end" => null "field_url" => "/10-klass/fizika/gelfgat-zadachnik/30-7" "field_display_title" => "30.7" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1239 #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 {#1248 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1244 #items: array:1 [ 0 => App\Models\Branch {#1126} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1242 #items: array:4 [ 0 => App\Models\Branch {#1126} 1 => App\Models\Branch {#1130} 2 => App\Models\Branch {#1134} 3 => App\Models\Branch {#1138} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1245 #items: array:2 [ 0 => App\Models\Element {#1107} 1 => App\Models\Element {#1099} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1319743" "type" => "task" ] "previous" => array:2 [ "refs" => "1319741" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1243 #items: array:1 [ 0 => App\Models\Book {#1056} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1341178" "type" => "book_page" ] ] #original: array:24 [ "id" => 1319742 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "217" "field_page_end" => null "field_url" => "/10-klass/fizika/gelfgat-zadachnik/30-7" "field_display_title" => "30.7" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1239} "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 {#1248} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1244} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1242} "content" => Illuminate\Database\Eloquent\Collection {#1245} "next" => array:2 [ "refs" => "1319743" "type" => "task" ] "previous" => array:2 [ "refs" => "1319741" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1243} "page" => array:2 [ "refs" => "1341178" "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 {#1253 #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" => 1319743 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "217" "field_page_end" => "218" "field_url" => "/10-klass/fizika/gelfgat-zadachnik/30-8" "field_display_title" => "30.8" "field_outside_task" => "0" "field_task_type" => Illuminate\Database\Eloquent\Collection {#1254 #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 {#1255 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1256 #items: array:1 [ 0 => App\Models\Branch {#1126} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1257 #items: array:4 [ 0 => App\Models\Branch {#1126} 1 => App\Models\Branch {#1130} 2 => App\Models\Branch {#1134} 3 => App\Models\Branch {#1138} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1259 #items: array:2 [ 0 => App\Models\Element {#1268 …30} 1 => App\Models\Element {#1270 …30} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1319744" "type" => "task" ] "previous" => array:2 [ "refs" => "1319742" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1265 #items: array:1 [ 0 => App\Models\Book {#1056} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1341178" "type" => "book_page" ] ] #original: array:24 [ "id" => 1319743 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "217" "field_page_end" => "218" "field_url" => "/10-klass/fizika/gelfgat-zadachnik/30-8" "field_display_title" => "30.8" "field_outside_task" => "0" "field_task_type" => Illuminate\Database\Eloquent\Collection {#1254} "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 {#1255} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1256} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1257} "content" => Illuminate\Database\Eloquent\Collection {#1259} "next" => array:2 [ "refs" => "1319744" "type" => "task" ] "previous" => array:2 [ "refs" => "1319742" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1265} "page" => array:2 [ "refs" => "1341178" "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 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:21 [ "id" => 1341178 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "217" "field_url" => "/10-klass/fizika/gelfgat-zadachnik/page-217" "field_display_title" => "217" "field_folder" => "1" "field_image_name" => "217" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1091} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1090} "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 {#1053} "content" => Illuminate\Database\Eloquent\Collection {#1122} "next" => array:2 [ "refs" => "1341179" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1341177" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1224} ] #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" => 1319742 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "217" "field_page_end" => null "field_url" => "/10-klass/fizika/gelfgat-zadachnik/30-7" "field_display_title" => "30.7" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037} "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} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1046} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1116} "content" => Illuminate\Database\Eloquent\Collection {#1038} "next" => array:2 [ "refs" => "1319743" "type" => "task" ] "previous" => array:2 [ "refs" => "1319741" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1110} "page" => array:2 [ "refs" => "1341178" "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 => "*" ] }
№30.7 (с. 217)
Условие. №30.7 (с. 217)
скриншот условия
30.7. Какой наименьшей кинетической энергией $W_k$ и скоростью $\text{v}$ должен обладать ион неона, чтобы при столкновении его с неподвижным нейтральным атомом неона могла произойти ионизация атома? Потенциал ионизации атомов неона $\varphi = 21,5$ В.
☑ $W_k = 43 \text{ эВ} = 6,9 \cdot 10^{8} \text{ Дж}$; 20 км/с.
Решение. Поскольку массы сталкивающихся частиц практически одинаковы, следует учесть кинетическую энергию, которую имеют частицы после столкновения. Наиболее эффективным для ионизации является неупругий удар, после которого обе частицы имеют одинаковую скорость, равную половине начальной скорости иона $v_0$. Суммарная кинетическая энергия частиц после неупругого удара $2 \cdot \frac{m_0 (v_0/2)^2}{2} = \frac{W_k}{2}$. Здесь $m_0 = M/N_A$ ($\text{M}$ — молярная масса неона). Согласно закону сохранения энергии: $W_k = e\varphi + W_k/2$.
Отсюда $W_k = 2e\varphi = 43 \text{ (эВ)} = 6,9 \cdot 10^{8} \text{ (Дж)}$ и $v = 2\sqrt{\frac{eN_A\varphi}{M}} = 2,0 \cdot 10^4 \text{ (м/с)}$.
Таким образом, для ионизации одного и того же атома ион должен иметь вдвое большую энергию, чем электрон.
Решение. №30.7 (с. 217)
Дано:
Потенциал ионизации атомов неона: $\phi = 21,5 \text{ В}$
Элементарный заряд: $e \approx 1,6 \cdot 10^{-19} \text{ Кл}$
Молярная масса неона: $M \approx 20,18 \cdot 10^{-3} \text{ кг/моль}$
Число Авогадро: $N_A \approx 6,022 \cdot 10^{23} \text{ моль}^{-1}$
Масса иона неона $m_1$ и масса атома неона $m_2$ приблизительно равны: $m_1 \approx m_2 = m$
Найти:
Наименьшая кинетическая энергия иона: $W_k$
Наименьшая скорость иона: $v$
Решение:
Для того чтобы произошла ионизация, часть кинетической энергии налетающего иона должна перейти во внутреннюю энергию атома, достаточную для отрыва электрона. Минимальная необходимая для этого энергия — это энергия ионизации $W_{ион} = e\phi$.
Вопрос стоит о наименьшей начальной энергии иона, при которой ионизация возможна. Это соответствует ситуации, когда максимальная доля начальной кинетической энергии переходит во внутреннюю. Такой процесс происходит при абсолютно неупругом ударе, когда после столкновения обе частицы (ион и атом) движутся вместе с одинаковой скоростью $u$.
Так как сталкиваются ион неона и нейтральный атом неона, их массы можно считать одинаковыми: $m_1 = m_2 = m$.
Запишем закон сохранения импульса для системы "ион-атом". Начальный импульс системы равен импульсу налетающего иона (так как атом покоится), а конечный импульс — это импульс двух слипшихся частиц.
$m v = (m + m) u$
$m v = 2m u$
Отсюда находим скорость частиц после столкновения:
$u = \frac{v}{2}$
Теперь запишем закон сохранения энергии. Начальная энергия системы — это кинетическая энергия иона $W_k$. После столкновения эта энергия перераспределяется между суммарной кинетической энергией двух частиц $W_{k'}$ и энергией, пошедшей на ионизацию атома $W_{ион}$.
$W_k = W_{k'} + W_{ион}$
Начальная кинетическая энергия иона:
$W_k = \frac{m v^2}{2}$
Конечная кинетическая энергия системы:
$W_{k'} = \frac{(m+m)u^2}{2} = \frac{2m(\frac{v}{2})^2}{2} = \frac{2m \frac{v^2}{4}}{2} = \frac{m v^2}{4}$
Сравнивая выражения для $W_k$ и $W_{k'}$, видим, что $W_{k'} = \frac{W_k}{2}$. Это означает, что при абсолютно неупругом столкновении двух тел равной массы половина начальной кинетической энергии переходит в кинетическую энергию системы после удара, а вторая половина может быть преобразована во внутреннюю энергию.
Подставим это в закон сохранения энергии:
$W_k = \frac{W_k}{2} + W_{ион}$
Отсюда минимальная энергия, необходимая для ионизации, равна:
$\frac{W_k}{2} = W_{ион} = e\phi$
$W_k = 2 e \phi$
Таким образом, наименьшая кинетическая энергия налетающего иона должна быть вдвое больше энергии ионизации атома.
Вычислим значение $W_k$ в электрон-вольтах (эВ) и в джоулях (Дж):
$W_k = 2 \cdot 21,5 \text{ эВ} = 43 \text{ эВ}$
$W_k = 2 \cdot (1,6 \cdot 10^{-19} \text{ Кл}) \cdot 21,5 \text{ В} = 6,88 \cdot 10^{-18} \text{ Дж} \approx 6,9 \cdot 10^{-18} \text{ Дж}$
Теперь найдем начальную скорость иона $v$ из формулы кинетической энергии $W_k = \frac{m v^2}{2}$.
$v = \sqrt{\frac{2 W_k}{m}}$
Массу атома неона $m$ найдем через молярную массу $M$ и число Авогадро $N_A$:
$m = \frac{M}{N_A} = \frac{20,18 \cdot 10^{-3} \text{ кг/моль}}{6,022 \cdot 10^{23} \text{ моль}^{-1}} \approx 3,35 \cdot 10^{-26} \text{ кг}$
Подставим значения и вычислим скорость:
$v = \sqrt{\frac{2 \cdot 6,9 \cdot 10^{-18} \text{ Дж}}{3,35 \cdot 10^{-26} \text{ кг}}} \approx \sqrt{4,12 \cdot 10^8 \frac{\text{м}^2}{\text{с}^2}} \approx 2,03 \cdot 10^4 \text{ м/с}$
Округлим результат:
$v \approx 2,0 \cdot 10^4 \text{ м/с} = 20 \text{ км/с}$
Ответ: $W_k = 43 \text{ эВ} \approx 6,9 \cdot 10^{-18} \text{ Дж}$; $v \approx 2,0 \cdot 10^4 \text{ м/с} = 20 \text{ км/с}$.
Другие задания:
Помогло решение? Оставьте отзыв в комментариях ниже.
Присоединяйтесь к Телеграм-группе @top_gdz
ПрисоединитьсяМы подготовили для вас ответ c подробным объяснением домашего задания по физике за 10-11 класс, для упражнения номер 30.7 расположенного на странице 217 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 №30.7 (с. 217), авторов: Гельфгат (Илья Маркович), Генденштейн (Лев Элевич), Кирик (Леонид Анатольевич), профильный уровень обучения учебного пособия издательства Илекса.