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Вариант 10, страница 89 - гдз по физике 9 класс дидактические материалы Марон, Марон
Авторы: Марон А. Е., Марон Е. А.
Тип: Дидактические материалы
Издательство: Просвещение
Год издания: 2022 - 2026
Уровень обучения: базовый
Цвет обложки: белый изображена башня
ISBN: 978-5-09-111414-0
Популярные ГДЗ в 9 классе
Самостоятельные работы. СР-16. Строение атома и атомного ядра - страница 89.
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" => 1428710 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "89" "field_page_end" => null "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy/cp16-10" "field_display_title" => "Вариант 10" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1036 #items: [] #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 {#1034 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1045 #items: array:1 [ 0 => App\Models\Branch {#1044 #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" => 1428174 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Самостоятельные работы" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1046 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "53" "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 {#1080 #items: array:1 [ 0 => App\Models\Book {#1047 #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" => 894 "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 {#1049 #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 {#1050 #items: array:1 [ 0 => 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: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 {#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" => 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 {#1054 #items: array:2 [ 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:12 [ "id" => 5107 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Марон" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Абрам" "field_patronymic" => "Евсеевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 5107 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Марон" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Абрам" "field_patronymic" => "Евсеевич" "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 {#1056 #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" => 5108 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Марон" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Евгений" "field_patronymic" => "Абрамович" "field_surname_rp" => null ] #original: array:12 [ "id" => 5108 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Марон" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Евгений" "field_patronymic" => "Абрамович" "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 {#1057 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1058 #items: array:1 [ 0 => 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:10 [ "id" => 6510 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Дидактические материалы" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "дидактические материалы" "field_creative_case" => "дидактическими материалами" "field_dative_case" => "дидактическим материалам" "field_genitive_case" => "дидактических материалов" "field_nominative_case" => "дидактические материалы" "field_prepositional_case" => "дидактических материалах" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "didakticheskie materialy" ] #original: array:10 [ "id" => 6510 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Дидактические материалы" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "дидактические материалы" "field_creative_case" => "дидактическими материалами" "field_dative_case" => "дидактическим материалам" "field_genitive_case" => "дидактических материалов" "field_nominative_case" => "дидактические материалы" "field_prepositional_case" => "дидактических материалах" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "didakticheskie materialy" ] #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 {#1060 #items: array:1 [ 0 => App\Models\Term {#1061 #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 {#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: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 {#1064 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1065 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => 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" => 38 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "базовый" "field_cases" => array:6 [ "field_accusative_case" => "базовый" "field_creative_case" => "базовым" "field_dative_case" => "базовому" "field_genitive_case" => "базового" "field_nominative_case" => "базовый" "field_prepositional_case" => "базовом" ] "field_translit" => "bazovyy" ] #original: array:6 [ "id" => 38 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "базовый" "field_cases" => array:6 [ "field_accusative_case" => "базовый" "field_creative_case" => "базовым" "field_dative_case" => "базовому" "field_genitive_case" => "базового" "field_nominative_case" => "базовый" "field_prepositional_case" => "базовом" ] "field_translit" => "bazovyy" ] #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 {#1068 #items: array:1 [ 0 => App\Models\Term {#1069 #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" => 25 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "ФГОС (новый)" "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" => "красный" "field_end_year" => "2027" "field_start_year" => "2023" "field_translit" => "fgos" "field_type" => "новый" ] #original: array:10 [ "id" => 25 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "ФГОС (новый)" "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" => "красный" "field_end_year" => "2027" "field_start_year" => "2023" "field_translit" => "fgos" "field_type" => "новый" ] #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" => "3" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1070 #items: array:1 [ 0 => App\Models\Term {#1071 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 34 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "переработанное" "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" => "pererabotannoe" ] #original: array:6 [ "id" => 34 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "переработанное" "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" => "pererabotannoe" ] #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 {#1072 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => "изображена башня" "field_publication_year" => "2022" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное пособие" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "674" "field_priority" => null "field_default_folder" => "/fizika_09/maron-dm/" "field_isbn" => "978-5-09-111414-0" "field_cover" => array:1 [ 0 => "/media/fizika_09/maron-dm/covers/cover1.webp?ts=1758533880" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_09/maron-dm/covers/cover1.webp?ts=1758533880" "alt" => "" "width" => "1888" "height" => "2427" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1073 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1074 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1075 #items: [] #escapeWhenCastingToString: false } "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1076 #items: array:1 [ 0 => App\Models\Term {#1077 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 45 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "белый" "field_cases" => array:6 [ "field_accusative_case" => "белый" "field_creative_case" => "белым" "field_dative_case" => "белому" "field_genitive_case" => "белого" "field_nominative_case" => "белый" "field_prepositional_case" => "белом" ] "field_translit" => "belyy" ] #original: array:6 [ "id" => 45 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "белый" "field_cases" => array:6 [ "field_accusative_case" => "белый" "field_creative_case" => "белым" "field_dative_case" => "белому" "field_genitive_case" => "белого" "field_nominative_case" => "белый" "field_prepositional_case" => "белом" ] "field_translit" => "belyy" ] #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" => 894 "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 {#1049} "field_class" => Illuminate\Database\Eloquent\Collection {#1050} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1052} "field_author" => Illuminate\Database\Eloquent\Collection {#1054} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1057} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1058} "field_country" => Illuminate\Database\Eloquent\Collection {#1060} "field_city" => Illuminate\Database\Eloquent\Collection {#1062} "field_series" => Illuminate\Database\Eloquent\Collection {#1064} "field_umk" => Illuminate\Database\Eloquent\Collection {#1065} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1066} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1068} "field_publication_number" => "3" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1070} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1072} "field_under_the_edition_degree" => null "field_cover_description" => "изображена башня" "field_publication_year" => "2022" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное пособие" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "674" "field_priority" => null "field_default_folder" => "/fizika_09/maron-dm/" "field_isbn" => "978-5-09-111414-0" "field_cover" => array:1 [ 0 => "/media/fizika_09/maron-dm/covers/cover1.webp?ts=1758533880" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_09/maron-dm/covers/cover1.webp?ts=1758533880" "alt" => "" "width" => "1888" "height" => "2427" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1073} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1074} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1075} "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1076} "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 {#1078 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1428174 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Самостоятельные работы" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1046} "field_page_start" => "53" "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 {#1080} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1078} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1110 #items: array:2 [ 0 => App\Models\Branch {#1118 #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" => 1428174 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Самостоятельные работы" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1119 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "53" "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 {#1120 #items: array:1 [ 0 => App\Models\Book {#1047} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1121 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1428174 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Самостоятельные работы" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1119} "field_page_start" => "53" "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 {#1120} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1121} ] #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 {#1122 #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" => 1428190 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "СР-16. Строение атома и атомного ядра" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1123 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "87" "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 {#1124 #items: array:1 [ 0 => App\Models\Book {#1047} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1125 #items: array:1 [ 0 => App\Models\Branch {#1044} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1428190 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "СР-16. Строение атома и атомного ядра" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1123} "field_page_start" => "87" "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 {#1124} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1125} ] #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 {#1037 #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" => 1683025 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1091 #items: array:1 [ 0 => App\Models\Edition {#1099 #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" => 5992 "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 {#1100 #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_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 {#1095 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1096 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 5992 "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 {#1095} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1096} "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" => "1428710" "type" => "task" ] "text" => "<p><strong>1.</strong> Определите состав ядра ${^{226}_{88}}\text{Ra}$.</p><p><strong>2.</strong> Напишите ядерную реакцию $\beta$-распада изотопа свинца ${^{209}_{82}}\text{Pb}$.</p><p><strong>3.</strong> Какова энергия связи ядра изотопа бора ${^{11}_{5}}\text{B}$? Масса протона 1,0073 а. е. м., масса нейтрона 1,0087 а. е. м., масса изотопа бора 11,00931 а. е. м.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "10-1.jpg" "alt" => null "width" => "1420" "height" => 465 "path" => "/media/fizika_09/maron-dm/0-cp16/10-1.webp?ts=1758964257" ] ] ] #original: array:7 [ "id" => 1683025 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1091} "task" => array:2 [ "refs" => "1428710" "type" => "task" ] "text" => "<p><strong>1.</strong> Определите состав ядра ${^{226}_{88}}\text{Ra}$.</p><p><strong>2.</strong> Напишите ядерную реакцию $\beta$-распада изотопа свинца ${^{209}_{82}}\text{Pb}$.</p><p><strong>3.</strong> Какова энергия связи ядра изотопа бора ${^{11}_{5}}\text{B}$? Масса протона 1,0073 а. е. м., масса нейтрона 1,0087 а. е. м., масса изотопа бора 11,00931 а. е. м.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "10-1.jpg" "alt" => null "width" => "1420" "height" => 465 "path" => "/media/fizika_09/maron-dm/0-cp16/10-1.webp?ts=1758964257" ] ] ] #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 {#1094 #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" => 1730727 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1085 #items: array:1 [ 0 => App\Models\Edition {#1093 #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" => 6313 "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 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 7012 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Gemini 2.5 Pro" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "gemini 2.5 pro" ] #original: array:6 [ "id" => 7012 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Gemini 2.5 Pro" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "gemini 2.5 pro" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1090 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1087 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1088 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 6313 "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 {#1087} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1088} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1428710" "type" => "task" ] "text" => "<p><strong>1.</strong> Определите состав ядра $_{88}^{226}\text{Ra}$.</p><p>Ядро атома обозначается как $_{Z}^{A}X$, где $\text{Z}$ - зарядовое число (количество протонов), а $\text{A}$ - массовое число (общее количество нуклонов, то есть протонов и нейтронов). Для ядра радия $_{88}^{226}\text{Ra}$ имеем:</p><p>Зарядовое число $Z = 88$. Это означает, что в ядре содержится 88 протонов.</p><p>Массовое число $A = 226$.</p><p>Число нейтронов $\text{N}$ можно найти по формуле $N = A - Z$.</p><p>$N = 226 - 88 = 138$.</p><p><strong>Ответ:</strong> Ядро $_{88}^{226}\text{Ra}$ состоит из 88 протонов и 138 нейтронов.</p><p><strong>2.</strong> Напишите ядерную реакцию $\beta$-распада изотопа свинца $_{82}^{209}\text{Pb}$.</p><p>$\beta$-распад (бета-минус распад) - это тип радиоактивного распада, при котором один из нейтронов ядра превращается в протон, при этом испускается электрон ($_{-1}^{0}e$ или $_{-1}^{0}\beta$) и электронное антинейтрино ($\bar{\nu}_e$).</p><p>Общая схема $\beta$-распада выглядит так: $_{Z}^{A}X \rightarrow _{Z+1}^{A}Y + _{-1}^{0}e + \bar{\nu}_e$.</p><p>В данном случае исходный изотоп - свинец-209 ($_{82}^{209}\text{Pb}$). Массовое число $A=209$ не изменяется. Зарядовое число $Z=82$ увеличивается на 1, становясь равным $82+1=83$. Элемент с зарядовым числом 83 - это висмут (Bi).</p><p>Таким образом, уравнение реакции $\beta$-распада для изотопа свинца-209:</p><p>$_{82}^{209}\text{Pb} \rightarrow _{83}^{209}\text{Bi} + _{-1}^{0}e + \bar{\nu}_e$</p><p><strong>Ответ:</strong> $_{82}^{209}\text{Pb} \rightarrow _{83}^{209}\text{Bi} + _{-1}^{0}e + \bar{\nu}_e$.</p><p><strong>3.</strong> Какова энергия связи ядра изотопа бора $_{5}^{11}$B? Масса протона 1,0073 а. е. м., масса нейтрона 1,0087 а. е. м., масса изотопа бора 11,00931 а. е. м.</p><p><strong>Дано:</strong></p><p>Изотоп бора: $_{5}^{11}\text{B}$<br>Масса протона, $m_p = 1,0073$ а. е. м.<br>Масса нейтрона, $m_n = 1,0087$ а. е. м.<br>Масса ядра бора, $M_я = 11,00931$ а. е. м.<br></p><p>$m_p = 1,0073 \text{ а. е. м.} \approx 1,6726 \cdot 10^{-27} \text{ кг}$<br>$m_n = 1,0087 \text{ а. е. м.} \approx 1,6749 \cdot 10^{-27} \text{ кг}$<br>$M_я = 11,00931 \text{ а. е. м.} \approx 1,8281 \cdot 10^{-26} \text{ кг}$</p><p><strong>Найти:</strong></p><p>Энергия связи, $E_{св}$.</p><p><strong>Решение:</strong></p><p><strong>1.</strong> Определим состав ядра бора $_{5}^{11}\text{B}$.<br>Число протонов $Z = 5$.<br>Число нейтронов $N = A - Z = 11 - 5 = 6$.</p><p><strong>2.</strong> Найдем дефект масс ($\Delta m$). Дефект масс - это разность между суммарной массой всех нуклонов (протонов и нейтронов), составляющих ядро, и реальной массой ядра.<br>Формула для дефекта масс:<br>$\Delta m = (Z \cdot m_p + N \cdot m_n) - M_я$<br>Подставим значения в а. е. м.:<br>$\Delta m = (5 \cdot 1,0073 + 6 \cdot 1,0087) - 11,00931$<br>$\Delta m = (5,0365 + 6,0522) - 11,00931$<br>$\Delta m = 11,0887 - 11,00931 = 0,07939 \text{ а. е. м.}$</p><p><strong>3.</strong> Рассчитаем энергию связи ($E_{св}$). Энергия связи - это энергия, которая выделяется при образовании ядра из отдельных нуклонов. Она равна энергии, соответствующей дефекту масс, и вычисляется по формуле Эйнштейна $E = \Delta m c^2$.<br>Для расчетов в атомных единицах массы удобно использовать энергетический эквивалент: 1 а. е. м. соответствует $931,5$ МэВ.<br>$E_{св} = \Delta m \cdot 931,5 \frac{\text{МэВ}}{\text{а.е.м.}}$<br>$E_{св} = 0,07939 \cdot 931,5 \text{ МэВ} \approx 73,95 \text{ МэВ}$.</p><p><strong>Ответ:</strong> Энергия связи ядра изотопа бора $_{5}^{11}\text{B}$ примерно равна $73,95$ МэВ.</p>" ] #original: array:6 [ "id" => 1730727 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1085} "task" => array:2 [ "refs" => "1428710" "type" => "task" ] "text" => "<p><strong>1.</strong> Определите состав ядра $_{88}^{226}\text{Ra}$.</p><p>Ядро атома обозначается как $_{Z}^{A}X$, где $\text{Z}$ - зарядовое число (количество протонов), а $\text{A}$ - массовое число (общее количество нуклонов, то есть протонов и нейтронов). Для ядра радия $_{88}^{226}\text{Ra}$ имеем:</p><p>Зарядовое число $Z = 88$. Это означает, что в ядре содержится 88 протонов.</p><p>Массовое число $A = 226$.</p><p>Число нейтронов $\text{N}$ можно найти по формуле $N = A - Z$.</p><p>$N = 226 - 88 = 138$.</p><p><strong>Ответ:</strong> Ядро $_{88}^{226}\text{Ra}$ состоит из 88 протонов и 138 нейтронов.</p><p><strong>2.</strong> Напишите ядерную реакцию $\beta$-распада изотопа свинца $_{82}^{209}\text{Pb}$.</p><p>$\beta$-распад (бета-минус распад) - это тип радиоактивного распада, при котором один из нейтронов ядра превращается в протон, при этом испускается электрон ($_{-1}^{0}e$ или $_{-1}^{0}\beta$) и электронное антинейтрино ($\bar{\nu}_e$).</p><p>Общая схема $\beta$-распада выглядит так: $_{Z}^{A}X \rightarrow _{Z+1}^{A}Y + _{-1}^{0}e + \bar{\nu}_e$.</p><p>В данном случае исходный изотоп - свинец-209 ($_{82}^{209}\text{Pb}$). Массовое число $A=209$ не изменяется. Зарядовое число $Z=82$ увеличивается на 1, становясь равным $82+1=83$. Элемент с зарядовым числом 83 - это висмут (Bi).</p><p>Таким образом, уравнение реакции $\beta$-распада для изотопа свинца-209:</p><p>$_{82}^{209}\text{Pb} \rightarrow _{83}^{209}\text{Bi} + _{-1}^{0}e + \bar{\nu}_e$</p><p><strong>Ответ:</strong> $_{82}^{209}\text{Pb} \rightarrow _{83}^{209}\text{Bi} + _{-1}^{0}e + \bar{\nu}_e$.</p><p><strong>3.</strong> Какова энергия связи ядра изотопа бора $_{5}^{11}$B? Масса протона 1,0073 а. е. м., масса нейтрона 1,0087 а. е. м., масса изотопа бора 11,00931 а. е. м.</p><p><strong>Дано:</strong></p><p>Изотоп бора: $_{5}^{11}\text{B}$<br>Масса протона, $m_p = 1,0073$ а. е. м.<br>Масса нейтрона, $m_n = 1,0087$ а. е. м.<br>Масса ядра бора, $M_я = 11,00931$ а. е. м.<br></p><p>$m_p = 1,0073 \text{ а. е. м.} \approx 1,6726 \cdot 10^{-27} \text{ кг}$<br>$m_n = 1,0087 \text{ а. е. м.} \approx 1,6749 \cdot 10^{-27} \text{ кг}$<br>$M_я = 11,00931 \text{ а. е. м.} \approx 1,8281 \cdot 10^{-26} \text{ кг}$</p><p><strong>Найти:</strong></p><p>Энергия связи, $E_{св}$.</p><p><strong>Решение:</strong></p><p><strong>1.</strong> Определим состав ядра бора $_{5}^{11}\text{B}$.<br>Число протонов $Z = 5$.<br>Число нейтронов $N = A - Z = 11 - 5 = 6$.</p><p><strong>2.</strong> Найдем дефект масс ($\Delta m$). Дефект масс - это разность между суммарной массой всех нуклонов (протонов и нейтронов), составляющих ядро, и реальной массой ядра.<br>Формула для дефекта масс:<br>$\Delta m = (Z \cdot m_p + N \cdot m_n) - M_я$<br>Подставим значения в а. е. м.:<br>$\Delta m = (5 \cdot 1,0073 + 6 \cdot 1,0087) - 11,00931$<br>$\Delta m = (5,0365 + 6,0522) - 11,00931$<br>$\Delta m = 11,0887 - 11,00931 = 0,07939 \text{ а. е. м.}$</p><p><strong>3.</strong> Рассчитаем энергию связи ($E_{св}$). Энергия связи - это энергия, которая выделяется при образовании ядра из отдельных нуклонов. Она равна энергии, соответствующей дефекту масс, и вычисляется по формуле Эйнштейна $E = \Delta m c^2$.<br>Для расчетов в атомных единицах массы удобно использовать энергетический эквивалент: 1 а. е. м. соответствует $931,5$ МэВ.<br>$E_{св} = \Delta m \cdot 931,5 \frac{\text{МэВ}}{\text{а.е.м.}}$<br>$E_{св} = 0,07939 \cdot 931,5 \text{ МэВ} \approx 73,95 \text{ МэВ}$.</p><p><strong>Ответ:</strong> Энергия связи ядра изотопа бора $_{5}^{11}\text{B}$ примерно равна $73,95$ 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" => "1428711" "type" => "task" ] "previous" => array:2 [ "refs" => "1428709" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1104 #items: array:1 [ 0 => App\Models\Book {#1047} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1042 #items: array:1 [ 0 => App\Models\BookPage {#1039 #connection: "mysql" #table: "book_pages" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 1428980 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "89" "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy/page-89" "field_display_title" => "89" "field_folder" => "1" "field_image_name" => "89" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1035 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1109 #items: array:1 [ 0 => App\Models\Book {#1047} ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "edition_groups" => Illuminate\Database\Eloquent\Collection {#1108 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1130 #items: array:1 [ 0 => App\Models\Element {#1129 #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" => 1683647 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1131 #items: array:1 [ 0 => App\Models\Edition {#1099} ] #escapeWhenCastingToString: false } "book_page" => array:2 [ "refs" => "1428980" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "89-1.jpg" "alt" => null "width" => "1595" "height" => 2530 "path" => "/media/fizika_09/maron-dm/0-1/89-1.webp?ts=1758964766" ] ] ] #original: array:6 [ "id" => 1683647 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1131} "book_page" => array:2 [ "refs" => "1428980" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "89-1.jpg" "alt" => null "width" => "1595" "height" => 2530 "path" => "/media/fizika_09/maron-dm/0-1/89-1.webp?ts=1758964766" ] ] ] #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" => "1428981" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1428979" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1193 #items: array:2 [ 0 => App\Models\Task {#1201 #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" => 1428709 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "88" "field_page_end" => "89" "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy/cp16-9" "field_display_title" => "Вариант 9" "field_outside_task" => "0" "field_task_type" => Illuminate\Database\Eloquent\Collection {#1202 #items: [] #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 {#1203 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1204 #items: array:1 [ 0 => App\Models\Branch {#1118} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1205 #items: array:2 [ 0 => App\Models\Branch {#1118} 1 => App\Models\Branch {#1122} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1207 #items: array:2 [ 0 => App\Models\Element {#1216 #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" => 1683024 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1217 #items: array:1 [ 0 => App\Models\Edition {#1099} ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1428709" "type" => "task" ] "text" => "<p><strong>1.</strong> Каков состав ядра $^{107}_{47}Ag$?</p><p><strong>2.</strong> Напишите ядерную реакцию $\alpha$-распада изотопа урана $^{238}_{92}U$.</p><p><strong>3.</strong> Рассчитайте энергию связи ядра изотопа кислорода $^{16}_8O$. Масса протона $1,0073$ а. е. м., масса нейтрона $1,0087$ а. е. м., масса изотопа кислорода $15,99491$ а. е. м.</p>" "img" => array:2 [ 0 => array:5 [ "name" => "9-1.jpg" "alt" => null "width" => "1437" "height" => 281 "path" => "/media/fizika_09/maron-dm/0-cp16/9-1.webp?ts=1758964257" ] 1 => array:5 [ "name" => "9-2.jpg" "alt" => null "width" => "1448" "height" => 271 "path" => "/media/fizika_09/maron-dm/0-cp16/9-2.webp?ts=1758964257" ] ] ] #original: array:7 [ "id" => 1683024 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1217} "task" => array:2 [ "refs" => "1428709" "type" => "task" ] "text" => "<p><strong>1.</strong> Каков состав ядра $^{107}_{47}Ag$?</p><p><strong>2.</strong> Напишите ядерную реакцию $\alpha$-распада изотопа урана $^{238}_{92}U$.</p><p><strong>3.</strong> Рассчитайте энергию связи ядра изотопа кислорода $^{16}_8O$. Масса протона $1,0073$ а. е. м., масса нейтрона $1,0087$ а. е. м., масса изотопа кислорода $15,99491$ а. е. м.</p>" "img" => array:2 [ 0 => array:5 [ "name" => "9-1.jpg" "alt" => null "width" => "1437" "height" => 281 "path" => "/media/fizika_09/maron-dm/0-cp16/9-1.webp?ts=1758964257" ] 1 => array:5 [ "name" => "9-2.jpg" "alt" => null "width" => "1448" "height" => 271 "path" => "/media/fizika_09/maron-dm/0-cp16/9-2.webp?ts=1758964257" ] ] ] #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 {#1218 #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" => 1730726 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1219 #items: array:1 [ 0 => App\Models\Edition {#1093} ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1428709" "type" => "task" ] "text" => "<p><strong>1.</strong> Каков состав ядра $^{107}_{47}$Ag?</p><p>Состав атомного ядра определяется его зарядовым (порядковым) числом $\text{Z}$ и массовым числом $\text{A}$. В стандартном обозначении изотопа $^{A}_{Z}X$, $\text{Z}$ (нижний индекс) — это число протонов, а $\text{A}$ (верхний индекс) — это общее число нуклонов (протонов и нейтронов).</p><p>Для изотопа серебра $^{107}_{47}$Ag:</p><p>Число протонов ($p^{+}$) равно зарядовому числу: $Z = 47$.</p><p>Массовое число (сумма протонов и нейтронов) равно: $A = 107$.</p><p>Число нейтронов ($n^{0}$) можно найти, вычтя число протонов из массового числа: $N = A - Z$.</p><p>$N = 107 - 47 = 60$.</p><p>Таким образом, ядро изотопа серебра-107 состоит из 47 протонов и 60 нейтронов.</p><p><strong>Ответ:</strong> Ядро изотопа серебра $^{107}_{47}$Ag состоит из 47 протонов и 60 нейтронов.</p><p><strong>2.</strong> Напишите ядерную реакцию α-распада изотопа урана $^{238}_{92}$U.</p><p>Альфа-распад (α-распад) — это тип радиоактивного распада, при котором ядро испускает альфа-частицу, которая является ядром атома гелия ($^{4}_{2}$He). В результате этого процесса массовое число исходного ядра уменьшается на 4, а зарядовое число — на 2.</p><p>Общая схема реакции α-распада:</p><p>$^{A}_{Z}X \rightarrow ^{A-4}_{Z-2}Y + ^{4}_{2}\text{He}$</p><p>Применим эту схему для изотопа урана $^{238}_{92}$U:</p><p>Исходное ядро: $A = 238$, $Z = 92$.</p><p>После распада образуется новое ядро Y с параметрами:</p><p>Новое массовое число: $A' = 238 - 4 = 234$.</p><p>Новое зарядовое число: $Z' = 92 - 2 = 90$.</p><p>Элемент с зарядовым числом 90 в периодической таблице Менделеева — это торий (Th).</p><p>Следовательно, в результате α-распада урана-238 образуется торий-234.</p><p>Полное уравнение ядерной реакции:</p><p>$^{238}_{92}\text{U} \rightarrow ^{234}_{90}\text{Th} + ^{4}_{2}\text{He}$</p><p><strong>Ответ:</strong> $^{238}_{92}\text{U} \rightarrow ^{234}_{90}\text{Th} + ^{4}_{2}\text{He}$.</p><p><strong>3.</strong> Рассчитайте энергию связи ядра изотопа кислорода $^{16}_{8}$O.</p><p><strong>Дано:</strong></p><p>Изотоп кислорода: $^{16}_{8}$O</p><p>Масса протона: $m_p = 1,0073$ а. е. м.</p><p>Масса нейтрона: $m_n = 1,0087$ а. е. м.</p><p>Масса ядра изотопа кислорода: $m_{я} = 15,99491$ а. е. м.</p><p>Справочные данные:</p><p>1 а. е. м. $= 1,66054 \times 10^{-27}$ кг</p><p>Скорость света в вакууме: $c = 2,9979 \times 10^8$ м/с</p><p><strong>В системе СИ:</strong></p><p>$m_p = 1,0073 \times 1,66054 \times 10^{-27} \text{ кг} \approx 1,6726 \times 10^{-27}$ кг</p><p>$m_n = 1,0087 \times 1,66054 \times 10^{-27} \text{ кг} \approx 1,6749 \times 10^{-27}$ кг</p><p>$m_{я} = 15,99491 \times 1,66054 \times 10^{-27} \text{ кг} \approx 2,6560 \times 10^{-26}$ кг</p><p><strong>Найти:</strong></p><p>$E_{св}$ — энергия связи ядра.</p><p><strong>Решение:</strong></p><p><strong>1.</strong> Определим состав ядра изотопа кислорода $^{16}_{8}$O.</p><p>Число протонов $Z = 8$.</p><p>Число нейтронов $N = A - Z = 16 - 8 = 8$.</p><p><strong>2.</strong> Рассчитаем дефект масс ($\Delta m$) — разность между суммой масс свободных нуклонов, составляющих ядро, и массой самого ядра. Для большей точности сначала вычислим дефект масс в атомных единицах массы (а. е. м.).</p><p>$\Delta m = (Z \cdot m_p + N \cdot m_n) - m_{я}$</p><p>$\Delta m = (8 \cdot 1,0073 \text{ а. е. м.} + 8 \cdot 1,0087 \text{ а. е. м.}) - 15,99491 \text{ а. е. м.}$</p><p>$\Delta m = (8,0584 + 8,0696) - 15,99491 = 16,1280 - 15,99491 = 0,13309$ а. е. м.</p><p><strong>3.</strong> Переведем дефект масс в единицы системы СИ (килограммы).</p><p>$\Delta m = 0,13309 \text{ а. е. м.} \times 1,66054 \times 10^{-27} \frac{\text{кг}}{\text{а. е. м.}} \approx 2,21 \times 10^{-28}$ кг.</p><p><strong>4.</strong> Энергия связи ($E_{св}$) вычисляется по формуле эквивалентности массы и энергии Эйнштейна:</p><p>$E_{св} = \Delta m \cdot c^2$</p><p>$E_{св} \approx 2,21 \times 10^{-28} \text{ кг} \times (2,9979 \times 10^8 \frac{\text{м}}{\text{с}})^2$</p><p>$E_{св} \approx 2,21 \times 10^{-28} \times 8,9874 \times 10^{16} \text{ Дж} \approx 1,986 \times 10^{-11}$ Дж.</p><p><strong>Ответ:</strong> $E_{св} \approx 1,986 \times 10^{-11}$ Дж.</p>" ] #original: array:6 [ "id" => 1730726 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1219} "task" => array:2 [ "refs" => "1428709" "type" => "task" ] "text" => "<p><strong>1.</strong> Каков состав ядра $^{107}_{47}$Ag?</p><p>Состав атомного ядра определяется его зарядовым (порядковым) числом $\text{Z}$ и массовым числом $\text{A}$. В стандартном обозначении изотопа $^{A}_{Z}X$, $\text{Z}$ (нижний индекс) — это число протонов, а $\text{A}$ (верхний индекс) — это общее число нуклонов (протонов и нейтронов).</p><p>Для изотопа серебра $^{107}_{47}$Ag:</p><p>Число протонов ($p^{+}$) равно зарядовому числу: $Z = 47$.</p><p>Массовое число (сумма протонов и нейтронов) равно: $A = 107$.</p><p>Число нейтронов ($n^{0}$) можно найти, вычтя число протонов из массового числа: $N = A - Z$.</p><p>$N = 107 - 47 = 60$.</p><p>Таким образом, ядро изотопа серебра-107 состоит из 47 протонов и 60 нейтронов.</p><p><strong>Ответ:</strong> Ядро изотопа серебра $^{107}_{47}$Ag состоит из 47 протонов и 60 нейтронов.</p><p><strong>2.</strong> Напишите ядерную реакцию α-распада изотопа урана $^{238}_{92}$U.</p><p>Альфа-распад (α-распад) — это тип радиоактивного распада, при котором ядро испускает альфа-частицу, которая является ядром атома гелия ($^{4}_{2}$He). В результате этого процесса массовое число исходного ядра уменьшается на 4, а зарядовое число — на 2.</p><p>Общая схема реакции α-распада:</p><p>$^{A}_{Z}X \rightarrow ^{A-4}_{Z-2}Y + ^{4}_{2}\text{He}$</p><p>Применим эту схему для изотопа урана $^{238}_{92}$U:</p><p>Исходное ядро: $A = 238$, $Z = 92$.</p><p>После распада образуется новое ядро Y с параметрами:</p><p>Новое массовое число: $A' = 238 - 4 = 234$.</p><p>Новое зарядовое число: $Z' = 92 - 2 = 90$.</p><p>Элемент с зарядовым числом 90 в периодической таблице Менделеева — это торий (Th).</p><p>Следовательно, в результате α-распада урана-238 образуется торий-234.</p><p>Полное уравнение ядерной реакции:</p><p>$^{238}_{92}\text{U} \rightarrow ^{234}_{90}\text{Th} + ^{4}_{2}\text{He}$</p><p><strong>Ответ:</strong> $^{238}_{92}\text{U} \rightarrow ^{234}_{90}\text{Th} + ^{4}_{2}\text{He}$.</p><p><strong>3.</strong> Рассчитайте энергию связи ядра изотопа кислорода $^{16}_{8}$O.</p><p><strong>Дано:</strong></p><p>Изотоп кислорода: $^{16}_{8}$O</p><p>Масса протона: $m_p = 1,0073$ а. е. м.</p><p>Масса нейтрона: $m_n = 1,0087$ а. е. м.</p><p>Масса ядра изотопа кислорода: $m_{я} = 15,99491$ а. е. м.</p><p>Справочные данные:</p><p>1 а. е. м. $= 1,66054 \times 10^{-27}$ кг</p><p>Скорость света в вакууме: $c = 2,9979 \times 10^8$ м/с</p><p><strong>В системе СИ:</strong></p><p>$m_p = 1,0073 \times 1,66054 \times 10^{-27} \text{ кг} \approx 1,6726 \times 10^{-27}$ кг</p><p>$m_n = 1,0087 \times 1,66054 \times 10^{-27} \text{ кг} \approx 1,6749 \times 10^{-27}$ кг</p><p>$m_{я} = 15,99491 \times 1,66054 \times 10^{-27} \text{ кг} \approx 2,6560 \times 10^{-26}$ кг</p><p><strong>Найти:</strong></p><p>$E_{св}$ — энергия связи ядра.</p><p><strong>Решение:</strong></p><p><strong>1.</strong> Определим состав ядра изотопа кислорода $^{16}_{8}$O.</p><p>Число протонов $Z = 8$.</p><p>Число нейтронов $N = A - Z = 16 - 8 = 8$.</p><p><strong>2.</strong> Рассчитаем дефект масс ($\Delta m$) — разность между суммой масс свободных нуклонов, составляющих ядро, и массой самого ядра. Для большей точности сначала вычислим дефект масс в атомных единицах массы (а. е. м.).</p><p>$\Delta m = (Z \cdot m_p + N \cdot m_n) - m_{я}$</p><p>$\Delta m = (8 \cdot 1,0073 \text{ а. е. м.} + 8 \cdot 1,0087 \text{ а. е. м.}) - 15,99491 \text{ а. е. м.}$</p><p>$\Delta m = (8,0584 + 8,0696) - 15,99491 = 16,1280 - 15,99491 = 0,13309$ а. е. м.</p><p><strong>3.</strong> Переведем дефект масс в единицы системы СИ (килограммы).</p><p>$\Delta m = 0,13309 \text{ а. е. м.} \times 1,66054 \times 10^{-27} \frac{\text{кг}}{\text{а. е. м.}} \approx 2,21 \times 10^{-28}$ кг.</p><p><strong>4.</strong> Энергия связи ($E_{св}$) вычисляется по формуле эквивалентности массы и энергии Эйнштейна:</p><p>$E_{св} = \Delta m \cdot c^2$</p><p>$E_{св} \approx 2,21 \times 10^{-28} \text{ кг} \times (2,9979 \times 10^8 \frac{\text{м}}{\text{с}})^2$</p><p>$E_{св} \approx 2,21 \times 10^{-28} \times 8,9874 \times 10^{16} \text{ Дж} \approx 1,986 \times 10^{-11}$ Дж.</p><p><strong>Ответ:</strong> $E_{св} \approx 1,986 \times 10^{-11}$ 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" => "1428710" "type" => "task" ] "previous" => array:2 [ "refs" => "1428708" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1213 #items: array:1 [ 0 => App\Models\Book {#1047} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1428979" "type" => "book_page" ] ] #original: array:24 [ "id" => 1428709 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "88" "field_page_end" => "89" "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy/cp16-9" "field_display_title" => "Вариант 9" "field_outside_task" => "0" "field_task_type" => 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Вариант 10 (с. 89)
Условие. Вариант 10 (с. 89)
скриншот условия
1. Определите состав ядра ${^{226}_{88}}\text{Ra}$.
2. Напишите ядерную реакцию $\beta$-распада изотопа свинца ${^{209}_{82}}\text{Pb}$.
3. Какова энергия связи ядра изотопа бора ${^{11}_{5}}\text{B}$? Масса протона 1,0073 а. е. м., масса нейтрона 1,0087 а. е. м., масса изотопа бора 11,00931 а. е. м.
Решение. Вариант 10 (с. 89)
1. Определите состав ядра $_{88}^{226}\text{Ra}$.
Ядро атома обозначается как $_{Z}^{A}X$, где $\text{Z}$ - зарядовое число (количество протонов), а $\text{A}$ - массовое число (общее количество нуклонов, то есть протонов и нейтронов). Для ядра радия $_{88}^{226}\text{Ra}$ имеем:
Зарядовое число $Z = 88$. Это означает, что в ядре содержится 88 протонов.
Массовое число $A = 226$.
Число нейтронов $\text{N}$ можно найти по формуле $N = A - Z$.
$N = 226 - 88 = 138$.
Ответ: Ядро $_{88}^{226}\text{Ra}$ состоит из 88 протонов и 138 нейтронов.
2. Напишите ядерную реакцию $\beta$-распада изотопа свинца $_{82}^{209}\text{Pb}$.
$\beta$-распад (бета-минус распад) - это тип радиоактивного распада, при котором один из нейтронов ядра превращается в протон, при этом испускается электрон ($_{-1}^{0}e$ или $_{-1}^{0}\beta$) и электронное антинейтрино ($\bar{\nu}_e$).
Общая схема $\beta$-распада выглядит так: $_{Z}^{A}X \rightarrow _{Z+1}^{A}Y + _{-1}^{0}e + \bar{\nu}_e$.
В данном случае исходный изотоп - свинец-209 ($_{82}^{209}\text{Pb}$). Массовое число $A=209$ не изменяется. Зарядовое число $Z=82$ увеличивается на 1, становясь равным $82+1=83$. Элемент с зарядовым числом 83 - это висмут (Bi).
Таким образом, уравнение реакции $\beta$-распада для изотопа свинца-209:
$_{82}^{209}\text{Pb} \rightarrow _{83}^{209}\text{Bi} + _{-1}^{0}e + \bar{\nu}_e$
Ответ: $_{82}^{209}\text{Pb} \rightarrow _{83}^{209}\text{Bi} + _{-1}^{0}e + \bar{\nu}_e$.
3. Какова энергия связи ядра изотопа бора $_{5}^{11}$B? Масса протона 1,0073 а. е. м., масса нейтрона 1,0087 а. е. м., масса изотопа бора 11,00931 а. е. м.
Дано:
Изотоп бора: $_{5}^{11}\text{B}$
Масса протона, $m_p = 1,0073$ а. е. м.
Масса нейтрона, $m_n = 1,0087$ а. е. м.
Масса ядра бора, $M_я = 11,00931$ а. е. м.
$m_p = 1,0073 \text{ а. е. м.} \approx 1,6726 \cdot 10^{-27} \text{ кг}$
$m_n = 1,0087 \text{ а. е. м.} \approx 1,6749 \cdot 10^{-27} \text{ кг}$
$M_я = 11,00931 \text{ а. е. м.} \approx 1,8281 \cdot 10^{-26} \text{ кг}$
Найти:
Энергия связи, $E_{св}$.
Решение:
1. Определим состав ядра бора $_{5}^{11}\text{B}$.
Число протонов $Z = 5$.
Число нейтронов $N = A - Z = 11 - 5 = 6$.
2. Найдем дефект масс ($\Delta m$). Дефект масс - это разность между суммарной массой всех нуклонов (протонов и нейтронов), составляющих ядро, и реальной массой ядра.
Формула для дефекта масс:
$\Delta m = (Z \cdot m_p + N \cdot m_n) - M_я$
Подставим значения в а. е. м.:
$\Delta m = (5 \cdot 1,0073 + 6 \cdot 1,0087) - 11,00931$
$\Delta m = (5,0365 + 6,0522) - 11,00931$
$\Delta m = 11,0887 - 11,00931 = 0,07939 \text{ а. е. м.}$
3. Рассчитаем энергию связи ($E_{св}$). Энергия связи - это энергия, которая выделяется при образовании ядра из отдельных нуклонов. Она равна энергии, соответствующей дефекту масс, и вычисляется по формуле Эйнштейна $E = \Delta m c^2$.
Для расчетов в атомных единицах массы удобно использовать энергетический эквивалент: 1 а. е. м. соответствует $931,5$ МэВ.
$E_{св} = \Delta m \cdot 931,5 \frac{\text{МэВ}}{\text{а.е.м.}}$
$E_{св} = 0,07939 \cdot 931,5 \text{ МэВ} \approx 73,95 \text{ МэВ}$.
Ответ: Энергия связи ядра изотопа бора $_{5}^{11}\text{B}$ примерно равна $73,95$ МэВ.
Другие задания:
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