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Номер 158, страница 279 - 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. 40. Физика атома и атомного ядра. Олимпиадные задачи - номер 158, страница 279.
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" => 1319850 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "279" "field_page_end" => "280" "field_url" => "/10-klass/fizika/gelfgat-zadachnik/olimp-158" "field_display_title" => "158" "field_outside_task" => "0" "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 {#1074 #items: array:1 [ 0 => App\Models\Branch {#1034 #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 {#1039 #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 {#1038 #items: array:1 [ 0 => App\Models\Book {#1040 #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 {#1041 #items: array:1 [ 0 => App\Models\Term {#1042 #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 [ …10] #original: array:10 [ …10] #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_class" => Illuminate\Database\Eloquent\Collection {#1043 #items: array:2 [ 0 => App\Models\Term {#1044 #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] } 1 => App\Models\Term {#1045 #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_publisher" => Illuminate\Database\Eloquent\Collection {#1046 #items: array:1 [ 0 => App\Models\Term {#1047 #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_author" => Illuminate\Database\Eloquent\Collection {#1048 #items: array:3 [ 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:12 [ …12] #original: array:12 [ …12] #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\Term {#1050 #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 [ …12] #original: array:12 [ …12] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 2 => App\Models\Term {#1051 #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 [ …12] #original: array:12 [ …12] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null …11 } ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1052 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1053 #items: array:1 [ 0 => App\Models\Term {#1054 …30} ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1055 #items: array:1 [ 0 => App\Models\Term {#1056 …30} ] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1057 #items: array:1 [ 0 => App\Models\Term {#1058 …30} ] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1059 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1060 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1061 #items: array:1 [ 0 => App\Models\Term {#1062 …30} ] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1063 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1064 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1065 #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 {#1066 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1067 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1068 #items: [] #escapeWhenCastingToString: false } "field_url" => "/10-klass/fizika/gelfgat-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1069 #items: array:1 [ 0 => App\Models\Term {#1070 …30} ] #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 {#1041} "field_class" => Illuminate\Database\Eloquent\Collection {#1043} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1046} "field_author" => Illuminate\Database\Eloquent\Collection {#1048} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1052} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1053} "field_country" => Illuminate\Database\Eloquent\Collection {#1055} "field_city" => Illuminate\Database\Eloquent\Collection {#1057} "field_series" => Illuminate\Database\Eloquent\Collection {#1059} "field_umk" => Illuminate\Database\Eloquent\Collection {#1060} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1061} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1063} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1064} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1065} "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 {#1066} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1067} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1068} "field_url" => "/10-klass/fizika/gelfgat-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1069} "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 {#1071 #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 {#1039} "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 {#1038} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1071} ] #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 {#1109 #items: array:3 [ 0 => App\Models\Branch {#1119 #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 {#1120 #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 {#1154 #items: array:1 [ 0 => App\Models\Book {#1121 #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 {#1123 #items: array:1 [ 0 => App\Models\Term {#1122 #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 {#1124 #items: array:2 [ 0 => App\Models\Term {#1125 #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 {#1126 #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 {#1127 #items: array:1 [ 0 => App\Models\Term {#1128 #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 {#1129 #items: array:3 [ 0 => App\Models\Term {#1130 #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 {#1131 #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 {#1132 #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 {#1133 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1134 #items: array:1 [ 0 => App\Models\Term {#1135 #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 {#1136 #items: array:1 [ 0 => App\Models\Term {#1137 #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 {#1138 #items: array:1 [ 0 => App\Models\Term {#1139 #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 {#1140 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1141 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1142 #items: array:1 [ 0 => App\Models\Term {#1143 #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 {#1144 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1145 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1146 #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 {#1147 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1148 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1149 #items: [] #escapeWhenCastingToString: false } "field_url" => "/10-klass/fizika/gelfgat-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1150 #items: array:1 [ 0 => App\Models\Term {#1151 #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 {#1123} "field_class" => Illuminate\Database\Eloquent\Collection {#1124} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1127} "field_author" => Illuminate\Database\Eloquent\Collection {#1129} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1133} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1134} "field_country" => Illuminate\Database\Eloquent\Collection {#1136} "field_city" => Illuminate\Database\Eloquent\Collection {#1138} "field_series" => Illuminate\Database\Eloquent\Collection {#1140} "field_umk" => Illuminate\Database\Eloquent\Collection {#1141} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1142} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1144} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1145} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1146} "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 {#1147} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1148} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1149} "field_url" => "/10-klass/fizika/gelfgat-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1150} "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 {#1152 #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 {#1120} "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 {#1154} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1152} ] #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 {#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" => 1319390 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "40. Физика атома и атомного ядра" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1155 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "275" "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 {#1121} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1157 #items: array:1 [ 0 => App\Models\Branch {#1034} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1319390 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "40. Физика атома и атомного ядра" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1155} "field_page_start" => "275" "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 => "*" ] } 2 => App\Models\Branch {#1158 #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" => 1319392 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Олимпиадные задачи" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1159 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "278" "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 {#1160 #items: array:1 [ 0 => App\Models\Book {#1121} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1169 #items: array:1 [ 0 => App\Models\Branch {#1168 #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" => 1319390 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "40. Физика атома и атомного ядра" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1170 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "275" "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 {#1171 #items: array:1 [ 0 => App\Models\Book {#1121} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1172 #items: array:1 [ 0 => App\Models\Branch {#1034} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1319390 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "40. Физика атома и атомного ядра" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1170} "field_page_start" => "275" "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 {#1171} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1172} ] #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" => 1319392 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Олимпиадные задачи" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1159} "field_page_start" => "278" "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 {#1160} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1169} ] #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 {#1072 #items: array:2 [ 0 => App\Models\Element {#1101 #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" => 1494136 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1091 #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" => 5430 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1097 #items: array:1 [ 0 => App\Models\Term {#1099 …30} ] #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 {#1098 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1096 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1095 #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 {#1097} "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 {#1098} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1096} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1095} "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" => "1319850" "type" => "task" ] "text" => "<p><strong>O58.</strong> Мишень из $^6\text{Li}$ подвергают бомбардировке нейтронами. Какова кинетическая энергия $W_n$ этих нейтронов, если в направлении движения нейтронов вылетают $\alpha$-частицы с кинетической энергией $W_\alpha = 3 \text{ МэВ}$? Энергией испускаемых $\gamma$-квантов можно пренебречь.</p><p>☑ 0,61 МэВ.</p><p><strong><em>Решение.</em></strong> В реакции $^6_3\text{Li} + ^1_0\text{n} \rightarrow ^3_1\text{H} + ^4_2\text{He}$ масса покоя частиц уменьшается на $\Delta m = 5,14 \cdot 10^{-3} \text{ а.е.м.}$, т. е. выделяется энергия $W = \Delta m \cdot c^2 = 4,8 \text{ МэВ}$. Движение частиц нерелятивистское; если не учитывать энергию, уносимую $\gamma$-излучением, закон сохранения энергии принимает вид $W_n + W = W_T + W_\alpha$, где $W_T$ — кинетическая энергия ядра трития. Используя также закон сохранения импульса, приходим к системе уравнений</p><p>$\begin{cases} \frac{m_n v_n^2}{2} - \frac{m_T v_T^2}{2} = W_\alpha - W, \\ m_n v_n = m_T v_T + m_\alpha v_\alpha. \end{cases}$</p><p>Обозначив $v_n/v_\alpha = x$ и принимая $m_T = 3m_n$, $m_\alpha = 4m_n$, получаем уравнение $x^2 + 4x - 14 + 6W/W_\alpha = 0$. Подставив числовые значения $\text{W}$ и $W_\alpha$, находим положительный корень этого уравнения $x = 0,9$. Следовательно,</p><p>$W_n = \frac{m_n v_n^2}{2} = \frac{x^2}{4} \cdot \frac{m_\alpha v_\alpha^2}{2} = \frac{x^2}{4} W_\alpha = 0,61 \text{ (МэВ)}$.</p>" "img" => array:2 [ 0 => array:5 [ "name" => "158-1.jpg" "alt" => null "width" => "1390" "height" => 1225 "path" => "/media/fizika_10/gelfgat-z/0-olimp/158-1.webp?ts=1756251295" ] 1 => array:5 [ "name" => "158-2.jpg" "alt" => null "width" => "1293" "height" => 344 "path" => "/media/fizika_10/gelfgat-z/0-olimp/158-2.webp?ts=1756251295" ] ] ] #original: array:7 [ "id" => 1494136 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1091} "task" => array:2 [ "refs" => "1319850" "type" => "task" ] "text" => "<p><strong>O58.</strong> Мишень из $^6\text{Li}$ подвергают бомбардировке нейтронами. Какова кинетическая энергия $W_n$ этих нейтронов, если в направлении движения нейтронов вылетают $\alpha$-частицы с кинетической энергией $W_\alpha = 3 \text{ МэВ}$? Энергией испускаемых $\gamma$-квантов можно пренебречь.</p><p>☑ 0,61 МэВ.</p><p><strong><em>Решение.</em></strong> В реакции $^6_3\text{Li} + ^1_0\text{n} \rightarrow ^3_1\text{H} + ^4_2\text{He}$ масса покоя частиц уменьшается на $\Delta m = 5,14 \cdot 10^{-3} \text{ а.е.м.}$, т. е. выделяется энергия $W = \Delta m \cdot c^2 = 4,8 \text{ МэВ}$. Движение частиц нерелятивистское; если не учитывать энергию, уносимую $\gamma$-излучением, закон сохранения энергии принимает вид $W_n + W = W_T + W_\alpha$, где $W_T$ — кинетическая энергия ядра трития. Используя также закон сохранения импульса, приходим к системе уравнений</p><p>$\begin{cases} \frac{m_n v_n^2}{2} - \frac{m_T v_T^2}{2} = W_\alpha - W, \\ m_n v_n = m_T v_T + m_\alpha v_\alpha. \end{cases}$</p><p>Обозначив $v_n/v_\alpha = x$ и принимая $m_T = 3m_n$, $m_\alpha = 4m_n$, получаем уравнение $x^2 + 4x - 14 + 6W/W_\alpha = 0$. Подставив числовые значения $\text{W}$ и $W_\alpha$, находим положительный корень этого уравнения $x = 0,9$. Следовательно,</p><p>$W_n = \frac{m_n v_n^2}{2} = \frac{x^2}{4} \cdot \frac{m_\alpha v_\alpha^2}{2} = \frac{x^2}{4} W_\alpha = 0,61 \text{ (МэВ)}$.</p>" "img" => array:2 [ 0 => array:5 [ "name" => "158-1.jpg" "alt" => null "width" => "1390" "height" => 1225 "path" => "/media/fizika_10/gelfgat-z/0-olimp/158-1.webp?ts=1756251295" ] 1 => array:5 [ "name" => "158-2.jpg" "alt" => null "width" => "1293" "height" => 344 "path" => "/media/fizika_10/gelfgat-z/0-olimp/158-2.webp?ts=1756251295" ] ] ] #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 {#1093 #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" => 1691693 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1085 #items: array:1 [ 0 => App\Models\Edition {#1094 #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 {#1089 #items: array:1 [ 0 => App\Models\Term {#1092 …30} ] #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 {#1090 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1088 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1084 #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 {#1089} "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 {#1090} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1088} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1084} "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" => "1319850" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Ядерная реакция: $^6_3Li + ^1_0n \rightarrow ^3_1H + ^4_2He$</p><p>Кинетическая энергия $\alpha$-частицы: $W_\alpha = 3$ МэВ</p><p>Энергетический выход реакции: $W = 4,8$ МэВ</p><p>Направление движения $\alpha$-частицы совпадает с направлением движения нейтрона.</p><p>Мишень ($^6_3Li$) до столкновения покоится.</p><p><strong>Найти:</strong></p><p>Кинетическую энергию нейтрона $W_n$.</p><p><strong>Решение:</strong></p><p>Для решения задачи используем законы сохранения энергии и импульса.</p><p><strong>1.</strong> <em>Закон сохранения энергии.</em></p><p>Суммарная энергия до реакции (энергия покоя частиц плюс кинетическая энергия нейтрона) равна суммарной энергии после реакции (энергия покоя продуктов плюс их кинетические энергии).</p><p>$E_{Li} + E_n + W_n = E_T + E_\alpha + W_T + W_\alpha$</p><p>Здесь $E$ - энергии покоя, $W$ - кинетические энергии. Индексы $n, Li, T, \alpha$ обозначают нейтрон, литий, тритий (ядро $^3_1H$) и альфа-частицу (ядро $^4_2He$) соответственно. Мишень лития покоится, поэтому ее кинетическая энергия равна нулю.</p><p>Разность энергий покоя до и после реакции — это энергетический выход реакции $W$:</p><p>$W = (E_{Li} + E_n) - (E_T + E_\alpha) = 4,8$ МэВ.</p><p>Тогда закон сохранения энергии принимает вид:</p><p>$W_n + W = W_T + W_\alpha$ (1)</p><p><strong>2.</strong> <em>Закон сохранения импульса.</em></p><p>Поскольку мишень покоилась, а частицы после реакции движутся в том же направлении, что и налетающий нейтрон, закон сохранения импульса в проекции на это направление выглядит так:</p><p>$p_n = p_T + p_\alpha$</p><p>Импульс $p$ связан с кинетической энергией $W_k$ и массой $m$ соотношением $p = \sqrt{2mW_k}$. Однако удобнее работать со скоростями.</p><p>$m_n v_n = m_T v_T + m_\alpha v_\alpha$ (2)</p><p>Для дальнейших расчетов воспользуемся приближенными значениями масс, выраженными через массу нейтрона $m_n$: масса трития $m_T \approx 3m_n$, масса альфа-частицы $m_\alpha \approx 4m_n$.</p><p>Из уравнения (2) выразим скорость трития $v_T$:</p><p>$m_T v_T = m_n v_n - m_\alpha v_\alpha \implies v_T = \frac{m_n v_n - m_\alpha v_\alpha}{m_T} = \frac{m_n v_n - 4m_n v_\alpha}{3m_n} = \frac{v_n - 4v_\alpha}{3}$</p><p>Теперь подставим это выражение в уравнение энергии (1), предварительно выразив его через скорости.</p><p>Из (1): $W_n - W_T = W_\alpha - W$</p><p>$\frac{m_n v_n^2}{2} - \frac{m_T v_T^2}{2} = W_\alpha - W$</p><p>$\frac{m_n v_n^2}{2} - \frac{3m_n}{2} \left( \frac{v_n - 4v_\alpha}{3} \right)^2 = W_\alpha - W$</p><p>$\frac{m_n v_n^2}{2} - \frac{3m_n(v_n - 4v_\alpha)^2}{18} = W_\alpha - W$</p><p>$\frac{m_n v_n^2}{2} - \frac{m_n(v_n^2 - 8v_n v_\alpha + 16v_\alpha^2)}{6} = W_\alpha - W$</p><p>Умножим все уравнение на 6:</p><p>$3m_n v_n^2 - m_n(v_n^2 - 8v_n v_\alpha + 16v_\alpha^2) = 6(W_\alpha - W)$</p><p>$2m_n v_n^2 + 8m_n v_n v_\alpha - 16m_n v_\alpha^2 = 6(W_\alpha - W)$</p><p>Разделим на 2:</p><p>$m_n v_n^2 + 4m_n v_n v_\alpha - 8m_n v_\alpha^2 = 3(W_\alpha - W)$</p><p>Введем отношение скоростей $x = v_n/v_\alpha$ и разделим уравнение на $m_n v_\alpha^2$:</p><p>$\left(\frac{v_n}{v_\alpha}\right)^2 + 4\left(\frac{v_n}{v_\alpha}\right) - 8 = \frac{3(W_\alpha - W)}{m_n v_\alpha^2}$</p><p>$x^2 + 4x - 8 = \frac{3(W_\alpha - W)}{m_n v_\alpha^2}$</p><p>Свяжем знаменатель правой части с известной величиной $W_\alpha$:</p><p>$W_\alpha = \frac{m_\alpha v_\alpha^2}{2} = \frac{4m_n v_\alpha^2}{2} = 2m_n v_\alpha^2 \implies m_n v_\alpha^2 = \frac{W_\alpha}{2}$</p><p>Подставим это в уравнение:</p><p>$x^2 + 4x - 8 = \frac{3(W_\alpha - W)}{W_\alpha/2} = \frac{6(W_\alpha - W)}{W_\alpha} = 6 - \frac{6W}{W_\alpha}$</p><p>Получаем квадратное уравнение относительно $x$:</p><p>$x^2 + 4x - 14 + \frac{6W}{W_\alpha} = 0$</p><p>Подставим числовые значения $W = 4,8$ МэВ и $W_\alpha = 3$ МэВ:</p><p>$x^2 + 4x - 14 + \frac{6 \cdot 4,8}{3} = 0$</p><p>$x^2 + 4x - 14 + 9,6 = 0$</p><p>$x^2 + 4x - 4,4 = 0$</p><p>Решим уравнение. Дискриминант $D = 4^2 - 4(1)(-4,4) = 16 + 17,6 = 33,6$.</p><p>Поскольку скорости $v_n$ и $v_\alpha$ сонаправлены, их отношение $x$ должно быть положительным. Берем корень со знаком плюс:</p><p>$x = \frac{-4 + \sqrt{33,6}}{2} \approx \frac{-4 + 5,797}{2} \approx 0,8985 \approx 0,9$</p><p>Теперь найдем кинетическую энергию нейтрона $W_n$. Установим связь между $W_n$ и $W_\alpha$:</p><p>$\frac{W_n}{W_\alpha} = \frac{m_n v_n^2 / 2}{m_\alpha v_\alpha^2 / 2} = \frac{m_n}{m_\alpha}\left(\frac{v_n}{v_\alpha}\right)^2 = \frac{m_n}{4m_n}x^2 = \frac{x^2}{4}$</p><p>Отсюда:</p><p>$W_n = W_\alpha \frac{x^2}{4} = 3 \text{ МэВ} \cdot \frac{0,9^2}{4} = 3 \cdot \frac{0,81}{4} = \frac{2,43}{4} \approx 0,6075$ МэВ.</p><p>Округляя до двух значащих цифр, получаем 0,61 МэВ.</p><p><strong>Ответ:</strong> 0,61 МэВ.</p>" ] #original: array:6 [ "id" => 1691693 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1085} "task" => array:2 [ "refs" => "1319850" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Ядерная реакция: $^6_3Li + ^1_0n \rightarrow ^3_1H + ^4_2He$</p><p>Кинетическая энергия $\alpha$-частицы: $W_\alpha = 3$ МэВ</p><p>Энергетический выход реакции: $W = 4,8$ МэВ</p><p>Направление движения $\alpha$-частицы совпадает с направлением движения нейтрона.</p><p>Мишень ($^6_3Li$) до столкновения покоится.</p><p><strong>Найти:</strong></p><p>Кинетическую энергию нейтрона $W_n$.</p><p><strong>Решение:</strong></p><p>Для решения задачи используем законы сохранения энергии и импульса.</p><p><strong>1.</strong> <em>Закон сохранения энергии.</em></p><p>Суммарная энергия до реакции (энергия покоя частиц плюс кинетическая энергия нейтрона) равна суммарной энергии после реакции (энергия покоя продуктов плюс их кинетические энергии).</p><p>$E_{Li} + E_n + W_n = E_T + E_\alpha + W_T + W_\alpha$</p><p>Здесь $E$ - энергии покоя, $W$ - кинетические энергии. Индексы $n, Li, T, \alpha$ обозначают нейтрон, литий, тритий (ядро $^3_1H$) и альфа-частицу (ядро $^4_2He$) соответственно. Мишень лития покоится, поэтому ее кинетическая энергия равна нулю.</p><p>Разность энергий покоя до и после реакции — это энергетический выход реакции $W$:</p><p>$W = (E_{Li} + E_n) - (E_T + E_\alpha) = 4,8$ МэВ.</p><p>Тогда закон сохранения энергии принимает вид:</p><p>$W_n + W = W_T + W_\alpha$ (1)</p><p><strong>2.</strong> <em>Закон сохранения импульса.</em></p><p>Поскольку мишень покоилась, а частицы после реакции движутся в том же направлении, что и налетающий нейтрон, закон сохранения импульса в проекции на это направление выглядит так:</p><p>$p_n = p_T + p_\alpha$</p><p>Импульс $p$ связан с кинетической энергией $W_k$ и массой $m$ соотношением $p = \sqrt{2mW_k}$. Однако удобнее работать со скоростями.</p><p>$m_n v_n = m_T v_T + m_\alpha v_\alpha$ (2)</p><p>Для дальнейших расчетов воспользуемся приближенными значениями масс, выраженными через массу нейтрона $m_n$: масса трития $m_T \approx 3m_n$, масса альфа-частицы $m_\alpha \approx 4m_n$.</p><p>Из уравнения (2) выразим скорость трития $v_T$:</p><p>$m_T v_T = m_n v_n - m_\alpha v_\alpha \implies v_T = \frac{m_n v_n - m_\alpha v_\alpha}{m_T} = \frac{m_n v_n - 4m_n v_\alpha}{3m_n} = \frac{v_n - 4v_\alpha}{3}$</p><p>Теперь подставим это выражение в уравнение энергии (1), предварительно выразив его через скорости.</p><p>Из (1): $W_n - W_T = W_\alpha - W$</p><p>$\frac{m_n v_n^2}{2} - \frac{m_T v_T^2}{2} = W_\alpha - W$</p><p>$\frac{m_n v_n^2}{2} - \frac{3m_n}{2} \left( \frac{v_n - 4v_\alpha}{3} \right)^2 = W_\alpha - W$</p><p>$\frac{m_n v_n^2}{2} - \frac{3m_n(v_n - 4v_\alpha)^2}{18} = W_\alpha - W$</p><p>$\frac{m_n v_n^2}{2} - \frac{m_n(v_n^2 - 8v_n v_\alpha + 16v_\alpha^2)}{6} = W_\alpha - W$</p><p>Умножим все уравнение на 6:</p><p>$3m_n v_n^2 - m_n(v_n^2 - 8v_n v_\alpha + 16v_\alpha^2) = 6(W_\alpha - W)$</p><p>$2m_n v_n^2 + 8m_n v_n v_\alpha - 16m_n v_\alpha^2 = 6(W_\alpha - W)$</p><p>Разделим на 2:</p><p>$m_n v_n^2 + 4m_n v_n v_\alpha - 8m_n v_\alpha^2 = 3(W_\alpha - W)$</p><p>Введем отношение скоростей $x = v_n/v_\alpha$ и разделим уравнение на $m_n v_\alpha^2$:</p><p>$\left(\frac{v_n}{v_\alpha}\right)^2 + 4\left(\frac{v_n}{v_\alpha}\right) - 8 = \frac{3(W_\alpha - W)}{m_n v_\alpha^2}$</p><p>$x^2 + 4x - 8 = \frac{3(W_\alpha - W)}{m_n v_\alpha^2}$</p><p>Свяжем знаменатель правой части с известной величиной $W_\alpha$:</p><p>$W_\alpha = \frac{m_\alpha v_\alpha^2}{2} = \frac{4m_n v_\alpha^2}{2} = 2m_n v_\alpha^2 \implies m_n v_\alpha^2 = \frac{W_\alpha}{2}$</p><p>Подставим это в уравнение:</p><p>$x^2 + 4x - 8 = \frac{3(W_\alpha - W)}{W_\alpha/2} = \frac{6(W_\alpha - W)}{W_\alpha} = 6 - \frac{6W}{W_\alpha}$</p><p>Получаем квадратное уравнение относительно $x$:</p><p>$x^2 + 4x - 14 + \frac{6W}{W_\alpha} = 0$</p><p>Подставим числовые значения $W = 4,8$ МэВ и $W_\alpha = 3$ МэВ:</p><p>$x^2 + 4x - 14 + \frac{6 \cdot 4,8}{3} = 0$</p><p>$x^2 + 4x - 14 + 9,6 = 0$</p><p>$x^2 + 4x - 4,4 = 0$</p><p>Решим уравнение. Дискриминант $D = 4^2 - 4(1)(-4,4) = 16 + 17,6 = 33,6$.</p><p>Поскольку скорости $v_n$ и $v_\alpha$ сонаправлены, их отношение $x$ должно быть положительным. Берем корень со знаком плюс:</p><p>$x = \frac{-4 + \sqrt{33,6}}{2} \approx \frac{-4 + 5,797}{2} \approx 0,8985 \approx 0,9$</p><p>Теперь найдем кинетическую энергию нейтрона $W_n$. Установим связь между $W_n$ и $W_\alpha$:</p><p>$\frac{W_n}{W_\alpha} = \frac{m_n v_n^2 / 2}{m_\alpha v_\alpha^2 / 2} = \frac{m_n}{m_\alpha}\left(\frac{v_n}{v_\alpha}\right)^2 = \frac{m_n}{4m_n}x^2 = \frac{x^2}{4}$</p><p>Отсюда:</p><p>$W_n = W_\alpha \frac{x^2}{4} = 3 \text{ МэВ} \cdot \frac{0,9^2}{4} = 3 \cdot \frac{0,81}{4} = \frac{2,43}{4} \approx 0,6075$ МэВ.</p><p>Округляя до двух значащих цифр, получаем 0,61 МэВ.</p><p><strong>Ответ:</strong> 0,61 МэВ.</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" => "1319851" "type" => "task" ] "previous" => array:2 [ "refs" => "1319849" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1104 #items: array:1 [ 0 => 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[] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] }
№158 (с. 279)
Условие. №158 (с. 279)
скриншот условия
O58. Мишень из $^6\text{Li}$ подвергают бомбардировке нейтронами. Какова кинетическая энергия $W_n$ этих нейтронов, если в направлении движения нейтронов вылетают $\alpha$-частицы с кинетической энергией $W_\alpha = 3 \text{ МэВ}$? Энергией испускаемых $\gamma$-квантов можно пренебречь.
☑ 0,61 МэВ.
Решение. В реакции $^6_3\text{Li} + ^1_0\text{n} \rightarrow ^3_1\text{H} + ^4_2\text{He}$ масса покоя частиц уменьшается на $\Delta m = 5,14 \cdot 10^{-3} \text{ а.е.м.}$, т. е. выделяется энергия $W = \Delta m \cdot c^2 = 4,8 \text{ МэВ}$. Движение частиц нерелятивистское; если не учитывать энергию, уносимую $\gamma$-излучением, закон сохранения энергии принимает вид $W_n + W = W_T + W_\alpha$, где $W_T$ — кинетическая энергия ядра трития. Используя также закон сохранения импульса, приходим к системе уравнений
$\begin{cases} \frac{m_n v_n^2}{2} - \frac{m_T v_T^2}{2} = W_\alpha - W, \\ m_n v_n = m_T v_T + m_\alpha v_\alpha. \end{cases}$
Обозначив $v_n/v_\alpha = x$ и принимая $m_T = 3m_n$, $m_\alpha = 4m_n$, получаем уравнение $x^2 + 4x - 14 + 6W/W_\alpha = 0$. Подставив числовые значения $\text{W}$ и $W_\alpha$, находим положительный корень этого уравнения $x = 0,9$. Следовательно,
$W_n = \frac{m_n v_n^2}{2} = \frac{x^2}{4} \cdot \frac{m_\alpha v_\alpha^2}{2} = \frac{x^2}{4} W_\alpha = 0,61 \text{ (МэВ)}$.
Решение. №158 (с. 279)
Дано:
Ядерная реакция: $^6_3Li + ^1_0n \rightarrow ^3_1H + ^4_2He$
Кинетическая энергия $\alpha$-частицы: $W_\alpha = 3$ МэВ
Энергетический выход реакции: $W = 4,8$ МэВ
Направление движения $\alpha$-частицы совпадает с направлением движения нейтрона.
Мишень ($^6_3Li$) до столкновения покоится.
Найти:
Кинетическую энергию нейтрона $W_n$.
Решение:
Для решения задачи используем законы сохранения энергии и импульса.
1. Закон сохранения энергии.
Суммарная энергия до реакции (энергия покоя частиц плюс кинетическая энергия нейтрона) равна суммарной энергии после реакции (энергия покоя продуктов плюс их кинетические энергии).
$E_{Li} + E_n + W_n = E_T + E_\alpha + W_T + W_\alpha$
Здесь $E$ - энергии покоя, $W$ - кинетические энергии. Индексы $n, Li, T, \alpha$ обозначают нейтрон, литий, тритий (ядро $^3_1H$) и альфа-частицу (ядро $^4_2He$) соответственно. Мишень лития покоится, поэтому ее кинетическая энергия равна нулю.
Разность энергий покоя до и после реакции — это энергетический выход реакции $W$:
$W = (E_{Li} + E_n) - (E_T + E_\alpha) = 4,8$ МэВ.
Тогда закон сохранения энергии принимает вид:
$W_n + W = W_T + W_\alpha$ (1)
2. Закон сохранения импульса.
Поскольку мишень покоилась, а частицы после реакции движутся в том же направлении, что и налетающий нейтрон, закон сохранения импульса в проекции на это направление выглядит так:
$p_n = p_T + p_\alpha$
Импульс $p$ связан с кинетической энергией $W_k$ и массой $m$ соотношением $p = \sqrt{2mW_k}$. Однако удобнее работать со скоростями.
$m_n v_n = m_T v_T + m_\alpha v_\alpha$ (2)
Для дальнейших расчетов воспользуемся приближенными значениями масс, выраженными через массу нейтрона $m_n$: масса трития $m_T \approx 3m_n$, масса альфа-частицы $m_\alpha \approx 4m_n$.
Из уравнения (2) выразим скорость трития $v_T$:
$m_T v_T = m_n v_n - m_\alpha v_\alpha \implies v_T = \frac{m_n v_n - m_\alpha v_\alpha}{m_T} = \frac{m_n v_n - 4m_n v_\alpha}{3m_n} = \frac{v_n - 4v_\alpha}{3}$
Теперь подставим это выражение в уравнение энергии (1), предварительно выразив его через скорости.
Из (1): $W_n - W_T = W_\alpha - W$
$\frac{m_n v_n^2}{2} - \frac{m_T v_T^2}{2} = W_\alpha - W$
$\frac{m_n v_n^2}{2} - \frac{3m_n}{2} \left( \frac{v_n - 4v_\alpha}{3} \right)^2 = W_\alpha - W$
$\frac{m_n v_n^2}{2} - \frac{3m_n(v_n - 4v_\alpha)^2}{18} = W_\alpha - W$
$\frac{m_n v_n^2}{2} - \frac{m_n(v_n^2 - 8v_n v_\alpha + 16v_\alpha^2)}{6} = W_\alpha - W$
Умножим все уравнение на 6:
$3m_n v_n^2 - m_n(v_n^2 - 8v_n v_\alpha + 16v_\alpha^2) = 6(W_\alpha - W)$
$2m_n v_n^2 + 8m_n v_n v_\alpha - 16m_n v_\alpha^2 = 6(W_\alpha - W)$
Разделим на 2:
$m_n v_n^2 + 4m_n v_n v_\alpha - 8m_n v_\alpha^2 = 3(W_\alpha - W)$
Введем отношение скоростей $x = v_n/v_\alpha$ и разделим уравнение на $m_n v_\alpha^2$:
$\left(\frac{v_n}{v_\alpha}\right)^2 + 4\left(\frac{v_n}{v_\alpha}\right) - 8 = \frac{3(W_\alpha - W)}{m_n v_\alpha^2}$
$x^2 + 4x - 8 = \frac{3(W_\alpha - W)}{m_n v_\alpha^2}$
Свяжем знаменатель правой части с известной величиной $W_\alpha$:
$W_\alpha = \frac{m_\alpha v_\alpha^2}{2} = \frac{4m_n v_\alpha^2}{2} = 2m_n v_\alpha^2 \implies m_n v_\alpha^2 = \frac{W_\alpha}{2}$
Подставим это в уравнение:
$x^2 + 4x - 8 = \frac{3(W_\alpha - W)}{W_\alpha/2} = \frac{6(W_\alpha - W)}{W_\alpha} = 6 - \frac{6W}{W_\alpha}$
Получаем квадратное уравнение относительно $x$:
$x^2 + 4x - 14 + \frac{6W}{W_\alpha} = 0$
Подставим числовые значения $W = 4,8$ МэВ и $W_\alpha = 3$ МэВ:
$x^2 + 4x - 14 + \frac{6 \cdot 4,8}{3} = 0$
$x^2 + 4x - 14 + 9,6 = 0$
$x^2 + 4x - 4,4 = 0$
Решим уравнение. Дискриминант $D = 4^2 - 4(1)(-4,4) = 16 + 17,6 = 33,6$.
Поскольку скорости $v_n$ и $v_\alpha$ сонаправлены, их отношение $x$ должно быть положительным. Берем корень со знаком плюс:
$x = \frac{-4 + \sqrt{33,6}}{2} \approx \frac{-4 + 5,797}{2} \approx 0,8985 \approx 0,9$
Теперь найдем кинетическую энергию нейтрона $W_n$. Установим связь между $W_n$ и $W_\alpha$:
$\frac{W_n}{W_\alpha} = \frac{m_n v_n^2 / 2}{m_\alpha v_\alpha^2 / 2} = \frac{m_n}{m_\alpha}\left(\frac{v_n}{v_\alpha}\right)^2 = \frac{m_n}{4m_n}x^2 = \frac{x^2}{4}$
Отсюда:
$W_n = W_\alpha \frac{x^2}{4} = 3 \text{ МэВ} \cdot \frac{0,9^2}{4} = 3 \cdot \frac{0,81}{4} = \frac{2,43}{4} \approx 0,6075$ МэВ.
Округляя до двух значащих цифр, получаем 0,61 МэВ.
Ответ: 0,61 МэВ.
Другие задания:
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