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Номер 2, страница 68, часть 3 - гдз по физике 9 класс рабочая тетрадь Грачев, Погожев
Авторы: Грачев А. В., Погожев В. А., Боков П. Ю., Вишнякова Е. А.
Тип: рабочая тетрадь
Издательство: Просвещение
Год издания: 2021 - 2026
Часть: 3
Цвет обложки: синий
ISBN: 978-5-09-098826-1 (ч.1) 978-5-09-098880-3 (ч.2) 978-5-09-098881-0 (ч.3)
Популярные ГДЗ в 9 классе
Часть 3. Глава 9. Физика атома и атомного ядра. Параграф 55. Ядерные силы. Энергия связи атомных ядер - номер 2, страница 68.
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" => 1435385 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "68" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/55-2" "field_display_title" => "2" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037 #items: array:1 [ 0 => App\Models\Term {#1036 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #original: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1035 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1046 #items: array:1 [ 0 => App\Models\Branch {#1045 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1434847 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "3" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1050 #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:7 [ "id" => 31 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Часть" "field_cases" => array:6 [ "field_accusative_case" => "Часть" "field_creative_case" => "Частью" "field_dative_case" => "Части" "field_genitive_case" => "Части" "field_nominative_case" => "Часть" "field_prepositional_case" => "Части" ] "field_page_check_not_needed" => "1" "field_short_name" => "ч." ] #original: array:7 [ "id" => 31 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Часть" "field_cases" => array:6 [ "field_accusative_case" => "Часть" "field_creative_case" => "Частью" "field_dative_case" => "Части" "field_genitive_case" => "Части" "field_nominative_case" => "Часть" "field_prepositional_case" => "Части" ] "field_page_check_not_needed" => "1" "field_short_name" => "ч." ] #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_page_start" => "3" "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 {#1083 #items: array:1 [ 0 => App\Models\Book {#1049 #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" => 1203 "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 {#1051 #items: array:1 [ 0 => App\Models\Term {#1048 #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 {#1052 #items: array:1 [ 0 => App\Models\Term {#1053 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5458 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "9" "field_cases" => array:6 [ "field_accusative_case" => "девятый" "field_creative_case" => "девятым" "field_dative_case" => "девятому" "field_genitive_case" => "девятого" "field_nominative_case" => "девятый" "field_prepositional_case" => "девятом" ] "field_translit" => "devjatyj" ] #original: array:6 [ "id" => 5458 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "9" "field_cases" => array:6 [ "field_accusative_case" => "девятый" "field_creative_case" => "девятым" "field_dative_case" => "девятому" "field_genitive_case" => "девятого" "field_nominative_case" => "девятый" "field_prepositional_case" => "девятом" ] "field_translit" => "devjatyj" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1054 #items: array:1 [ 0 => App\Models\Term {#1055 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5153 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Просвещение" "field_cases" => null "field_translit" => "prosveschenie" ] #original: array:6 [ "id" => 5153 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Просвещение" "field_cases" => null "field_translit" => "prosveschenie" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1056 #items: array:4 [ 0 => App\Models\Term {#1057 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 4180 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Грачев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Александр" "field_patronymic" => "Васильевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 4180 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Грачев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Александр" "field_patronymic" => "Васильевич" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Term {#1058 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 5484 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Погожев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Владимир" "field_patronymic" => "Александрович" "field_surname_rp" => null ] #original: array:12 [ "id" => 5484 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Погожев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Владимир" "field_patronymic" => "Александрович" "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 => "*" ] } 2 => App\Models\Term {#1059 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 3888 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Боков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Павел" "field_patronymic" => "Юрьевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 3888 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Боков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Павел" "field_patronymic" => "Юрьевич" "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 => "*" ] } 3 => 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:12 [ "id" => 4007 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Вишнякова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Екатерина" "field_patronymic" => "Анатольевна" "field_surname_rp" => null ] #original: array:12 [ "id" => 4007 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Вишнякова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Екатерина" "field_patronymic" => "Анатольевна" "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 {#1061 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1062 #items: array:1 [ 0 => App\Models\Term {#1063 #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" => 6736 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "рабочая тетрадь" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "рабочую тетрадь" "field_creative_case" => "рабочей тетрадью" "field_dative_case" => "рабочей тетради" "field_genitive_case" => "рабочей тетради" "field_nominative_case" => "рабочая тетрадь" "field_prepositional_case" => "рабочей тетради" ] "field_plural_form" => "рабочие тетради" "field_short_name" => "рт" "field_short_name_foreign" => null "field_translit" => "rabochaya tetrad" ] #original: array:10 [ "id" => 6736 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "рабочая тетрадь" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "рабочую тетрадь" "field_creative_case" => "рабочей тетрадью" "field_dative_case" => "рабочей тетради" "field_genitive_case" => "рабочей тетради" "field_nominative_case" => "рабочая тетрадь" "field_prepositional_case" => "рабочей тетради" ] "field_plural_form" => "рабочие тетради" "field_short_name" => "рт" "field_short_name_foreign" => null "field_translit" => "rabochaya tetrad" ] #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 {#1064 #items: array:1 [ 0 => App\Models\Term {#1065 #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 {#1066 #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 {#1068 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1069 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1070 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1071 #items: array:1 [ 0 => 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:10 [ "id" => 6706 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "ФГОС (старый)" "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_color" => null "field_end_year" => "2022" "field_start_year" => "2019" "field_translit" => "fgos-old" "field_type" => null ] #original: array:10 [ "id" => 6706 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "ФГОС (старый)" "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_color" => null "field_end_year" => "2022" "field_start_year" => "2019" "field_translit" => "fgos-old" "field_type" => 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_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1073 #items: array:1 [ 0 => App\Models\Term {#1074 #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" => 33 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "стереотипное" "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" => "stereotipnoe" ] #original: array:6 [ "id" => 33 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "стереотипное" "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" => "stereotipnoe" ] #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_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1075 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2021" "field_publication_year_until" => null "field_part" => "1, 2, 3" "field_part_writing" => "Часть" "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" => "594" "field_priority" => null "field_default_folder" => "/fizika_09/grachev-rt/" "field_isbn" => "978-5-09-098826-1 (ч.1) 978-5-09-098880-3 (ч.2) 978-5-09-098881-0 (ч.3)" "field_cover" => array:3 [ 0 => "/media/fizika_09/grachev-rt/covers/cover1.webp?ts=1759003248" 1 => "/media/fizika_09/grachev-rt/covers/cover2.webp?ts=1759003248" 2 => "/media/fizika_09/grachev-rt/covers/cover3.webp?ts=1759003248" ] "field_cover_alts" => array:3 [ 0 => "" 1 => "" 2 => "" ] "field_covers" => array:3 [ 0 => array:4 [ "path" => "/media/fizika_09/grachev-rt/covers/cover1.webp?ts=1759003248" "alt" => "" "width" => "2293" "height" => "2989" ] 1 => array:4 [ "path" => "/media/fizika_09/grachev-rt/covers/cover2.webp?ts=1759003248" "alt" => "" "width" => "2265" "height" => "3003" ] 2 => array:4 [ "path" => "/media/fizika_09/grachev-rt/covers/cover3.webp?ts=1759003248" "alt" => "" "width" => "2241" "height" => "2999" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1076 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1077 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1078 #items: [] #escapeWhenCastingToString: false } "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1079 #items: array:1 [ 0 => App\Models\Term {#1080 #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" => 49 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "синий" "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" => "siniy" ] #original: array:6 [ "id" => 49 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "синий" "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" => "siniy" ] #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" => 380 "subject" => 556 "class_subject" => 493 ] ] #original: array:50 [ "id" => 1203 "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 {#1051} "field_class" => Illuminate\Database\Eloquent\Collection {#1052} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1054} "field_author" => Illuminate\Database\Eloquent\Collection {#1056} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1061} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1062} "field_country" => Illuminate\Database\Eloquent\Collection {#1064} "field_city" => Illuminate\Database\Eloquent\Collection {#1066} "field_series" => Illuminate\Database\Eloquent\Collection {#1068} "field_umk" => Illuminate\Database\Eloquent\Collection {#1069} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1070} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1071} "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1073} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1075} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2021" "field_publication_year_until" => null "field_part" => "1, 2, 3" "field_part_writing" => "Часть" "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" => "594" "field_priority" => null "field_default_folder" => "/fizika_09/grachev-rt/" "field_isbn" => "978-5-09-098826-1 (ч.1) 978-5-09-098880-3 (ч.2) 978-5-09-098881-0 (ч.3)" "field_cover" => array:3 [ 0 => "/media/fizika_09/grachev-rt/covers/cover1.webp?ts=1759003248" 1 => "/media/fizika_09/grachev-rt/covers/cover2.webp?ts=1759003248" 2 => "/media/fizika_09/grachev-rt/covers/cover3.webp?ts=1759003248" ] "field_cover_alts" => array:3 [ 0 => "" 1 => "" 2 => "" ] "field_covers" => array:3 [ 0 => array:4 [ "path" => "/media/fizika_09/grachev-rt/covers/cover1.webp?ts=1759003248" "alt" => "" "width" => "2293" "height" => "2989" ] 1 => array:4 [ "path" => "/media/fizika_09/grachev-rt/covers/cover2.webp?ts=1759003248" "alt" => "" "width" => "2265" "height" => "3003" ] 2 => array:4 [ "path" => "/media/fizika_09/grachev-rt/covers/cover3.webp?ts=1759003248" "alt" => "" "width" => "2241" "height" => "2999" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1076} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1077} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1078} "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1079} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 380 "subject" => 556 "class_subject" => 493 ] ] #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 {#1081 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1434847 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "3" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1050} "field_page_start" => "3" "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 {#1083} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1081} ] #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 {#1114 #items: array:3 [ 0 => App\Models\Branch {#1124 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1434847 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "3" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1125 #items: array:1 [ 0 => App\Models\Term {#1047} ] #escapeWhenCastingToString: false } "field_page_start" => "3" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1126 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1127 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1434847 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "3" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1125} "field_page_start" => "3" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1126} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1127} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Branch {#1128 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1434866 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Физика атома и атомного ядра" "field_branch_order" => "9" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1132 #items: array:1 [ 0 => App\Models\Term {#1129 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ "field_accusative_case" => "Главу" "field_creative_case" => "Главой" "field_dative_case" => "Главе" "field_genitive_case" => "Главы" "field_nominative_case" => "Глава" "field_prepositional_case" => "Главе" ] "field_page_check_not_needed" => null "field_short_name" => null ] #original: array:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ "field_accusative_case" => "Главу" "field_creative_case" => "Главой" "field_dative_case" => "Главе" "field_genitive_case" => "Главы" "field_nominative_case" => "Глава" "field_prepositional_case" => "Главе" ] "field_page_check_not_needed" => null "field_short_name" => 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_page_start" => "60" "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 {#1131 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1130 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1434866 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Физика атома и атомного ядра" "field_branch_order" => "9" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1132} "field_page_start" => "60" "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 {#1131} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1130} ] #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 {#1133 #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" => 1434870 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Ядерные силы. Энергия связи атомных ядер" "field_branch_order" => "55" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1137 #items: array:1 [ 0 => App\Models\Term {#1134 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 32 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Параграф" "field_cases" => array:6 [ "field_accusative_case" => "Параграф" "field_creative_case" => "Параграфом" "field_dative_case" => "Параграфу" "field_genitive_case" => "Параграфа" "field_nominative_case" => "Параграф" "field_prepositional_case" => "Параграфе" ] "field_page_check_not_needed" => null "field_short_name" => "§" ] #original: array:7 [ "id" => 32 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Параграф" "field_cases" => array:6 [ "field_accusative_case" => "Параграф" "field_creative_case" => "Параграфом" "field_dative_case" => "Параграфу" "field_genitive_case" => "Параграфа" "field_nominative_case" => "Параграф" "field_prepositional_case" => "Параграфе" ] "field_page_check_not_needed" => null "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_page_start" => "67" "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 {#1049} ] #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" => 1434866 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Физика атома и атомного ядра" "field_branch_order" => "9" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1146 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_page_start" => "60" "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 [ …1] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1148 #items: array:1 [ …1] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1434866 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Физика атома и атомного ядра" "field_branch_order" => "9" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1146} "field_page_start" => "60" "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" => 1434870 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Ядерные силы. Энергия связи атомных ядер" "field_branch_order" => "55" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1137} "field_page_start" => "67" "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 => "*" ] } ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1038 #items: array:2 [ 0 => App\Models\Element {#1106 #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" => 1698773 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1098 #items: array:1 [ 0 => App\Models\Edition {#1104 #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" => 6173 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1102 #items: 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 {#1103 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1101 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1100 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 6173 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1102} "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 {#1103} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1101} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1100} "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" => "1435385" "type" => "task" ] "text" => "<p><strong>2.</strong> Определите дефект масс и энергию связи (в джоулях и мегаэлектронвольтах) ядер изотопов: а) $^{6}_{3}\text{Li}$; б) $^{10}_{5}\text{B}$; в) $^{14}_{7}\text{N}$; г*) $^{12}_{6}\text{C}$.</p><p>Для решения задачи воспользуйтесь таблицей 2 (см. приложение в конце рабочей тетради).</p><p><em>Решение.</em></p><p><em>Ответ:</em> ___________.</p>" "img" => array:2 [ 0 => array:5 [ "name" => "2-1.jpg" "alt" => null "width" => "2001" "height" => 452 "path" => "/media/fizika_09/grachev-rt/0-55/2-1.webp?ts=1759402909" ] 1 => array:5 [ "name" => "2-2.jpg" "alt" => null "width" => "1441" "height" => 171 "path" => "/media/fizika_09/grachev-rt/0-55/2-2.webp?ts=1759402909" ] ] ] #original: array:7 [ "id" => 1698773 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1098} "task" => array:2 [ "refs" => "1435385" "type" => "task" ] "text" => "<p><strong>2.</strong> Определите дефект масс и энергию связи (в джоулях и мегаэлектронвольтах) ядер изотопов: а) $^{6}_{3}\text{Li}$; б) $^{10}_{5}\text{B}$; в) $^{14}_{7}\text{N}$; г*) $^{12}_{6}\text{C}$.</p><p>Для решения задачи воспользуйтесь таблицей 2 (см. приложение в конце рабочей тетради).</p><p><em>Решение.</em></p><p><em>Ответ:</em> ___________.</p>" "img" => array:2 [ 0 => array:5 [ "name" => "2-1.jpg" "alt" => null "width" => "2001" "height" => 452 "path" => "/media/fizika_09/grachev-rt/0-55/2-1.webp?ts=1759402909" ] 1 => array:5 [ "name" => "2-2.jpg" "alt" => null "width" => "1441" "height" => 171 "path" => "/media/fizika_09/grachev-rt/0-55/2-2.webp?ts=1759402909" ] ] ] #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" => 1734759 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1090 #items: array:1 [ 0 => App\Models\Edition {#1097 #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" => 6327 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1096 #items: 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 {#1093 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1094 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1092 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 6327 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1096} "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 {#1093} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1094} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1092} "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" => "1435385" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p> <p> Масса протона, $m_p = 1.007276$ а.е.м. <br> Масса нейтрона, $m_n = 1.008665$ а.е.м. <br> Масса электрона, $m_e = 0.000549$ а.е.м. <br> Скорость света в вакууме, $c \approx 3 \cdot 10^8$ м/с <br> Атомная единица массы, 1 а.е.м. $= 1.66054 \cdot 10^{-27}$ кг <br> 1 МэВ $= 1.602 \cdot 10^{-13}$ Дж <br> Энергетический эквивалент 1 а.е.м. $ = 931.5$ МэВ </p> <p> Масса атома $^6_3\text{Li}$, $M_{Li} = 6.01512$ а.е.м. <br> Масса атома $^{10}_5\text{B}$, $M_{B} = 10.01294$ а.е.м. <br> Масса атома $^{14}_7\text{N}$, $M_{N} = 14.00307$ а.е.м. <br> Масса атома $^{12}_6\text{C}$, $M_{C} = 12.00000$ а.е.м. </p> <p><strong>Найти:</strong></p> <p>Дефект масс $\Delta m$ и энергию связи $E_{св}$ для ядер $^6_3\text{Li}$, $^{10}_5\text{B}$, $^{14}_7\text{N}$, $^{12}_6\text{C}$ в джоулях (Дж) и мегаэлектронвольтах (МэВ).</p> <p><strong>Решение:</strong></p> <p> Дефект масс ядра $\Delta m$ определяется как разность между суммой масс составляющих его нуклонов (протонов и нейтронов) и массой самого ядра $M_{ядра}$: <br> $\Delta m = Z \cdot m_p + N \cdot m_n - M_{ядра}$ <br> где $Z$ – число протонов, $N$ – число нейтронов ($N=A-Z$, где $A$ - массовое число). <br> Массу ядра можно найти, вычтя из массы нейтрального атома $M_{ат}$ массу его электронов: $M_{ядра} = M_{ат} - Z \cdot m_e$. <br> Энергия связи ядра $E_{св}$ связана с дефектом масс соотношением Эйнштейна $E = mc^2$: <br> $E_{св} = \Delta m \cdot c^2$ <br> Для вычисления энергии в МэВ используется формула: $E_{св} (\text{МэВ}) = \Delta m (\text{а.е.м.}) \cdot 931.5 \text{ МэВ/а.е.м.}$. <br> Для перевода в джоули используется соотношение 1 МэВ = $1.602 \cdot 10^{-13}$ Дж. </p> <p><strong>а) $^6_3\text{Li}$</strong></p> <p> Ядро лития-6 состоит из $Z=3$ протонов и $N=6-3=3$ нейтронов. <br> Масса ядра лития: $M_{ядра, Li} = M_{Li} - Z \cdot m_e = 6.01512 - 3 \cdot 0.000549 = 6.01512 - 0.001647 = 6.013473$ а.е.м. <br> Суммарная масса нуклонов: $Z \cdot m_p + N \cdot m_n = 3 \cdot 1.007276 + 3 \cdot 1.008665 = 3.021828 + 3.025995 = 6.047823$ а.е.м. <br> Дефект масс: $\Delta m = 6.047823 - 6.013473 = 0.03435$ а.е.м. <br> Энергия связи в МэВ: $E_{св} = 0.03435 \cdot 931.5 \approx 32.00$ МэВ. <br> Энергия связи в Дж: $E_{св} = 32.00 \cdot 1.602 \cdot 10^{-13} \approx 5.126 \cdot 10^{-12}$ Дж. <br> <strong>Ответ:</strong> $\Delta m = 0.03435$ а.е.м.; $E_{св} = 32.00$ МэВ; $E_{св} \approx 5.13 \cdot 10^{-12}$ Дж. </p> <p><strong>б) $^{10}_5\text{B}$</strong></p> <p> Ядро бора-10 состоит из $Z=5$ протонов и $N=10-5=5$ нейтронов. <br> Масса ядра бора: $M_{ядра, B} = M_{B} - Z \cdot m_e = 10.01294 - 5 \cdot 0.000549 = 10.01294 - 0.002745 = 10.010195$ а.е.м. <br> Суммарная масса нуклонов: $Z \cdot m_p + N \cdot m_n = 5 \cdot 1.007276 + 5 \cdot 1.008665 = 5.03638 + 5.043325 = 10.079705$ а.е.м. <br> Дефект масс: $\Delta m = 10.079705 - 10.010195 = 0.06951$ а.е.м. <br> Энергия связи в МэВ: $E_{св} = 0.06951 \cdot 931.5 \approx 64.75$ МэВ. <br> Энергия связи в Дж: $E_{св} = 64.75 \cdot 1.602 \cdot 10^{-13} \approx 1.037 \cdot 10^{-11}$ Дж. <br> <strong>Ответ:</strong> $\Delta m = 0.06951$ а.е.м.; $E_{св} = 64.75$ МэВ; $E_{св} \approx 1.04 \cdot 10^{-11}$ Дж. </p> <p><strong>в) $^{14}_7\text{N}$</strong></p> <p> Ядро азота-14 состоит из $Z=7$ протонов и $N=14-7=7$ нейтронов. <br> Масса ядра азота: $M_{ядра, N} = M_{N} - Z \cdot m_e = 14.00307 - 7 \cdot 0.000549 = 14.00307 - 0.003843 = 13.999227$ а.е.м. <br> Суммарная масса нуклонов: $Z \cdot m_p + N \cdot m_n = 7 \cdot 1.007276 + 7 \cdot 1.008665 = 7.050932 + 7.060655 = 14.111587$ а.е.м. <br> Дефект масс: $\Delta m = 14.111587 - 13.999227 = 0.11236$ а.е.м. <br> Энергия связи в МэВ: $E_{св} = 0.11236 \cdot 931.5 \approx 104.66$ МэВ. <br> Энергия связи в Дж: $E_{св} = 104.66 \cdot 1.602 \cdot 10^{-13} \approx 1.677 \cdot 10^{-11}$ Дж. <br> <strong>Ответ:</strong> $\Delta m = 0.11236$ а.е.м.; $E_{св} = 104.66$ МэВ; $E_{св} \approx 1.68 \cdot 10^{-11}$ Дж. </p> <p><strong>г*) $^{12}_6\text{C}$</strong></p> <p> Ядро углерода-12 состоит из $Z=6$ протонов и $N=12-6=6$ нейтронов. <br> Масса ядра углерода: $M_{ядра, C} = M_{C} - Z \cdot m_e = 12.00000 - 6 \cdot 0.000549 = 12.00000 - 0.003294 = 11.996706$ а.е.м. <br> Суммарная масса нуклонов: $Z \cdot m_p + N \cdot m_n = 6 \cdot 1.007276 + 6 \cdot 1.008665 = 6.043656 + 6.05199 = 12.095646$ а.е.м. <br> Дефект масс: $\Delta m = 12.095646 - 11.996706 = 0.09894$ а.е.м. <br> Энергия связи в МэВ: $E_{св} = 0.09894 \cdot 931.5 \approx 92.16$ МэВ. <br> Энергия связи в Дж: $E_{св} = 92.16 \cdot 1.602 \cdot 10^{-13} \approx 1.476 \cdot 10^{-11}$ Дж. <br> <strong>Ответ:</strong> $\Delta m = 0.09894$ а.е.м.; $E_{св} = 92.16$ МэВ; $E_{св} \approx 1.48 \cdot 10^{-11}$ Дж. </p>" ] #original: array:6 [ "id" => 1734759 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1090} "task" => array:2 [ "refs" => "1435385" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p> <p> Масса протона, $m_p = 1.007276$ а.е.м. <br> Масса нейтрона, $m_n = 1.008665$ а.е.м. <br> Масса электрона, $m_e = 0.000549$ а.е.м. <br> Скорость света в вакууме, $c \approx 3 \cdot 10^8$ м/с <br> Атомная единица массы, 1 а.е.м. $= 1.66054 \cdot 10^{-27}$ кг <br> 1 МэВ $= 1.602 \cdot 10^{-13}$ Дж <br> Энергетический эквивалент 1 а.е.м. $ = 931.5$ МэВ </p> <p> Масса атома $^6_3\text{Li}$, $M_{Li} = 6.01512$ а.е.м. <br> Масса атома $^{10}_5\text{B}$, $M_{B} = 10.01294$ а.е.м. <br> Масса атома $^{14}_7\text{N}$, $M_{N} = 14.00307$ а.е.м. <br> Масса атома $^{12}_6\text{C}$, $M_{C} = 12.00000$ а.е.м. </p> <p><strong>Найти:</strong></p> <p>Дефект масс $\Delta m$ и энергию связи $E_{св}$ для ядер $^6_3\text{Li}$, $^{10}_5\text{B}$, $^{14}_7\text{N}$, $^{12}_6\text{C}$ в джоулях (Дж) и мегаэлектронвольтах (МэВ).</p> <p><strong>Решение:</strong></p> <p> Дефект масс ядра $\Delta m$ определяется как разность между суммой масс составляющих его нуклонов (протонов и нейтронов) и массой самого ядра $M_{ядра}$: <br> $\Delta m = Z \cdot m_p + N \cdot m_n - M_{ядра}$ <br> где $Z$ – число протонов, $N$ – число нейтронов ($N=A-Z$, где $A$ - массовое число). <br> Массу ядра можно найти, вычтя из массы нейтрального атома $M_{ат}$ массу его электронов: $M_{ядра} = M_{ат} - Z \cdot m_e$. <br> Энергия связи ядра $E_{св}$ связана с дефектом масс соотношением Эйнштейна $E = mc^2$: <br> $E_{св} = \Delta m \cdot c^2$ <br> Для вычисления энергии в МэВ используется формула: $E_{св} (\text{МэВ}) = \Delta m (\text{а.е.м.}) \cdot 931.5 \text{ МэВ/а.е.м.}$. <br> Для перевода в джоули используется соотношение 1 МэВ = $1.602 \cdot 10^{-13}$ Дж. </p> <p><strong>а) $^6_3\text{Li}$</strong></p> <p> Ядро лития-6 состоит из $Z=3$ протонов и $N=6-3=3$ нейтронов. <br> Масса ядра лития: $M_{ядра, Li} = M_{Li} - Z \cdot m_e = 6.01512 - 3 \cdot 0.000549 = 6.01512 - 0.001647 = 6.013473$ а.е.м. <br> Суммарная масса нуклонов: $Z \cdot m_p + N \cdot m_n = 3 \cdot 1.007276 + 3 \cdot 1.008665 = 3.021828 + 3.025995 = 6.047823$ а.е.м. <br> Дефект масс: $\Delta m = 6.047823 - 6.013473 = 0.03435$ а.е.м. <br> Энергия связи в МэВ: $E_{св} = 0.03435 \cdot 931.5 \approx 32.00$ МэВ. <br> Энергия связи в Дж: $E_{св} = 32.00 \cdot 1.602 \cdot 10^{-13} \approx 5.126 \cdot 10^{-12}$ Дж. <br> <strong>Ответ:</strong> $\Delta m = 0.03435$ а.е.м.; $E_{св} = 32.00$ МэВ; $E_{св} \approx 5.13 \cdot 10^{-12}$ Дж. </p> <p><strong>б) $^{10}_5\text{B}$</strong></p> <p> Ядро бора-10 состоит из $Z=5$ протонов и $N=10-5=5$ нейтронов. <br> Масса ядра бора: $M_{ядра, B} = M_{B} - Z \cdot m_e = 10.01294 - 5 \cdot 0.000549 = 10.01294 - 0.002745 = 10.010195$ а.е.м. <br> Суммарная масса нуклонов: $Z \cdot m_p + N \cdot m_n = 5 \cdot 1.007276 + 5 \cdot 1.008665 = 5.03638 + 5.043325 = 10.079705$ а.е.м. <br> Дефект масс: $\Delta m = 10.079705 - 10.010195 = 0.06951$ а.е.м. <br> Энергия связи в МэВ: $E_{св} = 0.06951 \cdot 931.5 \approx 64.75$ МэВ. <br> Энергия связи в Дж: $E_{св} = 64.75 \cdot 1.602 \cdot 10^{-13} \approx 1.037 \cdot 10^{-11}$ Дж. <br> <strong>Ответ:</strong> $\Delta m = 0.06951$ а.е.м.; $E_{св} = 64.75$ МэВ; $E_{св} \approx 1.04 \cdot 10^{-11}$ Дж. </p> <p><strong>в) $^{14}_7\text{N}$</strong></p> <p> Ядро азота-14 состоит из $Z=7$ протонов и $N=14-7=7$ нейтронов. <br> Масса ядра азота: $M_{ядра, N} = M_{N} - Z \cdot m_e = 14.00307 - 7 \cdot 0.000549 = 14.00307 - 0.003843 = 13.999227$ а.е.м. <br> Суммарная масса нуклонов: $Z \cdot m_p + N \cdot m_n = 7 \cdot 1.007276 + 7 \cdot 1.008665 = 7.050932 + 7.060655 = 14.111587$ а.е.м. <br> Дефект масс: $\Delta m = 14.111587 - 13.999227 = 0.11236$ а.е.м. <br> Энергия связи в МэВ: $E_{св} = 0.11236 \cdot 931.5 \approx 104.66$ МэВ. <br> Энергия связи в Дж: $E_{св} = 104.66 \cdot 1.602 \cdot 10^{-13} \approx 1.677 \cdot 10^{-11}$ Дж. <br> <strong>Ответ:</strong> $\Delta m = 0.11236$ а.е.м.; $E_{св} = 104.66$ МэВ; $E_{св} \approx 1.68 \cdot 10^{-11}$ Дж. </p> <p><strong>г*) $^{12}_6\text{C}$</strong></p> <p> Ядро углерода-12 состоит из $Z=6$ протонов и $N=12-6=6$ нейтронов. <br> Масса ядра углерода: $M_{ядра, C} = M_{C} - Z \cdot m_e = 12.00000 - 6 \cdot 0.000549 = 12.00000 - 0.003294 = 11.996706$ а.е.м. <br> Суммарная масса нуклонов: $Z \cdot m_p + N \cdot m_n = 6 \cdot 1.007276 + 6 \cdot 1.008665 = 6.043656 + 6.05199 = 12.095646$ а.е.м. <br> Дефект масс: $\Delta m = 12.095646 - 11.996706 = 0.09894$ а.е.м. <br> Энергия связи в МэВ: $E_{св} = 0.09894 \cdot 931.5 \approx 92.16$ МэВ. <br> Энергия связи в Дж: $E_{св} = 92.16 \cdot 1.602 \cdot 10^{-13} \approx 1.476 \cdot 10^{-11}$ Дж. <br> <strong>Ответ:</strong> $\Delta m = 0.09894$ а.е.м.; $E_{св} = 92.16$ МэВ; $E_{св} \approx 1.48 \cdot 10^{-11}$ Дж. </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" => "1435386" "type" => "task" ] "previous" => array:2 [ "refs" => "1435384" "type" => 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№2 (с. 68)
Условие. №2 (с. 68)
скриншот условия
2. Определите дефект масс и энергию связи (в джоулях и мегаэлектронвольтах) ядер изотопов: а) $^{6}_{3}\text{Li}$; б) $^{10}_{5}\text{B}$; в) $^{14}_{7}\text{N}$; г*) $^{12}_{6}\text{C}$.
Для решения задачи воспользуйтесь таблицей 2 (см. приложение в конце рабочей тетради).
Решение.
Ответ: ___________.
Решение. №2 (с. 68)
Дано:
Масса протона, $m_p = 1.007276$ а.е.м.
Масса нейтрона, $m_n = 1.008665$ а.е.м.
Масса электрона, $m_e = 0.000549$ а.е.м.
Скорость света в вакууме, $c \approx 3 \cdot 10^8$ м/с
Атомная единица массы, 1 а.е.м. $= 1.66054 \cdot 10^{-27}$ кг
1 МэВ $= 1.602 \cdot 10^{-13}$ Дж
Энергетический эквивалент 1 а.е.м. $ = 931.5$ МэВ
Масса атома $^6_3\text{Li}$, $M_{Li} = 6.01512$ а.е.м.
Масса атома $^{10}_5\text{B}$, $M_{B} = 10.01294$ а.е.м.
Масса атома $^{14}_7\text{N}$, $M_{N} = 14.00307$ а.е.м.
Масса атома $^{12}_6\text{C}$, $M_{C} = 12.00000$ а.е.м.
Найти:
Дефект масс $\Delta m$ и энергию связи $E_{св}$ для ядер $^6_3\text{Li}$, $^{10}_5\text{B}$, $^{14}_7\text{N}$, $^{12}_6\text{C}$ в джоулях (Дж) и мегаэлектронвольтах (МэВ).
Решение:
Дефект масс ядра $\Delta m$ определяется как разность между суммой масс составляющих его нуклонов (протонов и нейтронов) и массой самого ядра $M_{ядра}$:
$\Delta m = Z \cdot m_p + N \cdot m_n - M_{ядра}$
где $Z$ – число протонов, $N$ – число нейтронов ($N=A-Z$, где $A$ - массовое число).
Массу ядра можно найти, вычтя из массы нейтрального атома $M_{ат}$ массу его электронов: $M_{ядра} = M_{ат} - Z \cdot m_e$.
Энергия связи ядра $E_{св}$ связана с дефектом масс соотношением Эйнштейна $E = mc^2$:
$E_{св} = \Delta m \cdot c^2$
Для вычисления энергии в МэВ используется формула: $E_{св} (\text{МэВ}) = \Delta m (\text{а.е.м.}) \cdot 931.5 \text{ МэВ/а.е.м.}$.
Для перевода в джоули используется соотношение 1 МэВ = $1.602 \cdot 10^{-13}$ Дж.
а) $^6_3\text{Li}$
Ядро лития-6 состоит из $Z=3$ протонов и $N=6-3=3$ нейтронов.
Масса ядра лития: $M_{ядра, Li} = M_{Li} - Z \cdot m_e = 6.01512 - 3 \cdot 0.000549 = 6.01512 - 0.001647 = 6.013473$ а.е.м.
Суммарная масса нуклонов: $Z \cdot m_p + N \cdot m_n = 3 \cdot 1.007276 + 3 \cdot 1.008665 = 3.021828 + 3.025995 = 6.047823$ а.е.м.
Дефект масс: $\Delta m = 6.047823 - 6.013473 = 0.03435$ а.е.м.
Энергия связи в МэВ: $E_{св} = 0.03435 \cdot 931.5 \approx 32.00$ МэВ.
Энергия связи в Дж: $E_{св} = 32.00 \cdot 1.602 \cdot 10^{-13} \approx 5.126 \cdot 10^{-12}$ Дж.
Ответ: $\Delta m = 0.03435$ а.е.м.; $E_{св} = 32.00$ МэВ; $E_{св} \approx 5.13 \cdot 10^{-12}$ Дж.
б) $^{10}_5\text{B}$
Ядро бора-10 состоит из $Z=5$ протонов и $N=10-5=5$ нейтронов.
Масса ядра бора: $M_{ядра, B} = M_{B} - Z \cdot m_e = 10.01294 - 5 \cdot 0.000549 = 10.01294 - 0.002745 = 10.010195$ а.е.м.
Суммарная масса нуклонов: $Z \cdot m_p + N \cdot m_n = 5 \cdot 1.007276 + 5 \cdot 1.008665 = 5.03638 + 5.043325 = 10.079705$ а.е.м.
Дефект масс: $\Delta m = 10.079705 - 10.010195 = 0.06951$ а.е.м.
Энергия связи в МэВ: $E_{св} = 0.06951 \cdot 931.5 \approx 64.75$ МэВ.
Энергия связи в Дж: $E_{св} = 64.75 \cdot 1.602 \cdot 10^{-13} \approx 1.037 \cdot 10^{-11}$ Дж.
Ответ: $\Delta m = 0.06951$ а.е.м.; $E_{св} = 64.75$ МэВ; $E_{св} \approx 1.04 \cdot 10^{-11}$ Дж.
в) $^{14}_7\text{N}$
Ядро азота-14 состоит из $Z=7$ протонов и $N=14-7=7$ нейтронов.
Масса ядра азота: $M_{ядра, N} = M_{N} - Z \cdot m_e = 14.00307 - 7 \cdot 0.000549 = 14.00307 - 0.003843 = 13.999227$ а.е.м.
Суммарная масса нуклонов: $Z \cdot m_p + N \cdot m_n = 7 \cdot 1.007276 + 7 \cdot 1.008665 = 7.050932 + 7.060655 = 14.111587$ а.е.м.
Дефект масс: $\Delta m = 14.111587 - 13.999227 = 0.11236$ а.е.м.
Энергия связи в МэВ: $E_{св} = 0.11236 \cdot 931.5 \approx 104.66$ МэВ.
Энергия связи в Дж: $E_{св} = 104.66 \cdot 1.602 \cdot 10^{-13} \approx 1.677 \cdot 10^{-11}$ Дж.
Ответ: $\Delta m = 0.11236$ а.е.м.; $E_{св} = 104.66$ МэВ; $E_{св} \approx 1.68 \cdot 10^{-11}$ Дж.
г*) $^{12}_6\text{C}$
Ядро углерода-12 состоит из $Z=6$ протонов и $N=12-6=6$ нейтронов.
Масса ядра углерода: $M_{ядра, C} = M_{C} - Z \cdot m_e = 12.00000 - 6 \cdot 0.000549 = 12.00000 - 0.003294 = 11.996706$ а.е.м.
Суммарная масса нуклонов: $Z \cdot m_p + N \cdot m_n = 6 \cdot 1.007276 + 6 \cdot 1.008665 = 6.043656 + 6.05199 = 12.095646$ а.е.м.
Дефект масс: $\Delta m = 12.095646 - 11.996706 = 0.09894$ а.е.м.
Энергия связи в МэВ: $E_{св} = 0.09894 \cdot 931.5 \approx 92.16$ МэВ.
Энергия связи в Дж: $E_{св} = 92.16 \cdot 1.602 \cdot 10^{-13} \approx 1.476 \cdot 10^{-11}$ Дж.
Ответ: $\Delta m = 0.09894$ а.е.м.; $E_{св} = 92.16$ МэВ; $E_{св} \approx 1.48 \cdot 10^{-11}$ Дж.
Другие задания:
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