Номер 2, страница 323 - гдз по физике 9 класс учебник Грачев, Погожев

Физика, 9 класс Учебник, авторы: Грачев Александр Васильевич, Погожев Владимир Александрович, Боков Павел Юрьевич, издательство Вентана-граф, Москва, 2012

Авторы: Грачев А. В., Погожев В. А., Боков П. Ю.

Тип: Учебник

Серия: алгоритм успеха

Издательство: Вентана-граф

Год издания: 2012 - 2026

Цвет обложки: синий изображено здание и радуга

ISBN: 978-5-360-07412-0

Глава 9. Физика атома и атомного ядра. Параграф 54. Ядерные силы. Энергия связи атомных ядер. Упражнения - номер 2, страница 323.

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" => 1438565
    "created_at" => "2026-04-10 13:58:26"
    "updated_at" => null
    "field_page_start" => "323"
    "field_page_end" => null
    "field_url" => "/9-klass/fizika/grachev-uchebnik/54upr-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: []
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          #attributeCastCache: []
          #dateFormat: null
          #appends: []
          #dispatchesEvents: []
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          #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" => 1438011
            "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 {#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" => 29
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Глава"
                    "field_cases" => array:6 [ …6]
                    "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 [ …6]
                    "field_page_check_not_needed" => null
                    "field_short_name" => null
                  ]
                  #changes: []
                  #casts: []
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                  #dateFormat: null
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                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
            }
            "field_page_start" => "307"
            "field_branch_display" => "0"
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            "field_display_task_interval" => "0"
            "field_display_branch_page" => "1"
            "field_branch_title_in_content" => "0"
            "field_navigation_title" => null
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            "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" => 1202
                    "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 [ …6]
                            "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 [ …6]
                            "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 [ …6]
                            "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 [ …6]
                            "field_translit" => "devjatyj"
                          ]
                          #changes: []
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                          #dateFormat: null
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                          #touches: []
                          +timestamps: true
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                          #hidden: []
                          #visible: []
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                          #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" => 5174
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Вентана-граф"
                            "field_cases" => null
                            "field_translit" => "ventana-graf"
                          ]
                          #original: array:6 [
                            "id" => 5174
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Вентана-граф"
                            "field_cases" => null
                            "field_translit" => "ventana-graf"
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_author" => Illuminate\Database\Eloquent\Collection {#1056
                      #items: array:3 [
                        0 => App\Models\Term {#1057
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:12 [
                            "id" => 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
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                          #dispatchesEvents: []
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                          #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
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                          #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: []
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                          #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
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                          #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: []
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                          #attributeCastCache: []
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                          #touches: []
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                          #hidden: []
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                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1060
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_book_type" => Illuminate\Database\Eloquent\Collection {#1061
                      #items: array:1 [
                        0 => App\Models\Term {#1062
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
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                          #escapeWhenCastingToString: false
                          #attributes: array:10 [
                            "id" => 6671
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Учебник"
                            "field_book_type_foreign" => null
                            "field_cases" => array:6 [ …6]
                            "field_plural_form" => null
                            "field_short_name" => null
                            "field_short_name_foreign" => null
                            "field_translit" => "uchebnik"
                          ]
                          #original: array:10 [
                            "id" => 6671
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Учебник"
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                    "field_country" => Illuminate\Database\Eloquent\Collection {#1063
                      #items: array:1 [
                        0 => App\Models\Term {#1064
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
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                          +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 [ …6]
                            "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 [ …6]
                            "field_translit" => "rossiya"
                          ]
                          #changes: []
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                    "field_city" => Illuminate\Database\Eloquent\Collection {#1065
                      #items: array:1 [
                        0 => App\Models\Term {#1066
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:6 [
                            "id" => 15
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Москва"
                            "field_cases" => array:6 [ …6]
                            "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 [ …6]
                            "field_translit" => "moskva"
                          ]
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                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
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                          #relations: []
                          #touches: []
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                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_series" => Illuminate\Database\Eloquent\Collection {#1067
                      #items: array:1 [
                        0 => App\Models\Term {#1068
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:8 [
                            "id" => 4697
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "алгоритм успеха"
                            "field_cases" => null
                            "field_foreign_lang_series" => null
                            "field_transcription_eng" => null
                            "field_translit" => "algoritm uspekha"
                          ]
                          #original: array:8 [
                            "id" => 4697
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "алгоритм успеха"
                            "field_cases" => null
                            "field_foreign_lang_series" => null
                            "field_transcription_eng" => null
                            "field_translit" => "algoritm uspekha"
                          ]
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                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #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 [ …6]
                            "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 [ …6]
                            "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" => "2"
                    "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" => 6900
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "доработанное"
                            "field_cases" => array:6 [ …6]
                            "field_translit" => "dorabotannoe"
                          ]
                          #original: array:6 [
                            "id" => 6900
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "доработанное"
                            "field_cases" => array:6 [ …6]
                            "field_translit" => "dorabotannoe"
                          ]
                          #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" => "изображено здание и радуга"
                    "field_publication_year" => "2012"
                    "field_publication_year_until" => null
                    "field_part" => ""
                    "field_part_writing" => ""
                    "field_second_foreign_language" => null
                    "field_for_whom" => "Учебник для учащихся общеобразовательных организаций"
                    "field_allowed" => null
                    "field_reserve_field" => null
                    "field_link_to_source" => null
                    "field_tasks_count" => "580"
                    "field_priority" => null
                    "field_default_folder" => "/fizika_09/grachev-u/"
                    "field_isbn" => "978-5-360-07412-0"
                    "field_cover" => array:1 [
                      0 => "/media/fizika_09/grachev-u/covers/cover1.webp?ts=1759082140"
                    ]
                    "field_cover_alts" => array:1 [
                      0 => ""
                    ]
                    "field_covers" => array:1 [
                      0 => array:4 [
                        "path" => "/media/fizika_09/grachev-u/covers/cover1.webp?ts=1759082140"
                        "alt" => ""
                        "width" => "2294"
                        "height" => "3039"
                      ]
                    ]
                    "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-uchebnik"
                    "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 [ …6]
                            "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 [ …6]
                            "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" => 1202
                    "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 {#1060}
                    "field_book_type" => Illuminate\Database\Eloquent\Collection {#1061}
                    "field_country" => Illuminate\Database\Eloquent\Collection {#1063}
                    "field_city" => Illuminate\Database\Eloquent\Collection {#1065}
                    "field_series" => Illuminate\Database\Eloquent\Collection {#1067}
                    "field_umk" => Illuminate\Database\Eloquent\Collection {#1069}
                    "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1070}
                    "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1071}
                    "field_publication_number" => "2"
                    "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" => "изображено здание и радуга"
                    "field_publication_year" => "2012"
                    "field_publication_year_until" => null
                    "field_part" => ""
                    "field_part_writing" => ""
                    "field_second_foreign_language" => null
                    "field_for_whom" => "Учебник для учащихся общеобразовательных организаций"
                    "field_allowed" => null
                    "field_reserve_field" => null
                    "field_link_to_source" => null
                    "field_tasks_count" => "580"
                    "field_priority" => null
                    "field_default_folder" => "/fizika_09/grachev-u/"
                    "field_isbn" => "978-5-360-07412-0"
                    "field_cover" => array:1 [
                      0 => "/media/fizika_09/grachev-u/covers/cover1.webp?ts=1759082140"
                    ]
                    "field_cover_alts" => array:1 [
                      0 => ""
                    ]
                    "field_covers" => array:1 [
                      0 => array:4 [
                        "path" => "/media/fizika_09/grachev-u/covers/cover1.webp?ts=1759082140"
                        "alt" => ""
                        "width" => "2294"
                        "height" => "3039"
                      ]
                    ]
                    "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-uchebnik"
                    "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: []
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                  #attributeCastCache: []
                  #dateFormat: null
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                  #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" => 1438011
            "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 {#1050}
            "field_page_start" => "307"
            "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" => 1438011
            "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 {#1125
              #items: array:1 [
                0 => App\Models\Term {#1047}
              ]
              #escapeWhenCastingToString: false
            }
            "field_page_start" => "307"
            "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" => 1438011
            "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 {#1125}
            "field_page_start" => "307"
            "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" => 1438018
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => "Ядерные силы. Энергия связи атомных ядер"
            "field_branch_order" => "54"
            "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" => 32
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Параграф"
                    "field_cases" => array:6 [ …6]
                    "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 [ …6]
                    "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" => "318"
            "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" => 1438018
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => "Ядерные силы. Энергия связи атомных ядер"
            "field_branch_order" => "54"
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            "text" => "<p><strong>2.</strong> Определите массу ядра атома кислорода ${}_{8}^{16}\text{O}$, если известно, что его удельная энергия связи равна $7,9761$ МэВ/нуклон.</p>"
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            "task" => array:2 [
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            "text" => "<p><strong>2.</strong> Определите массу ядра атома кислорода ${}_{8}^{16}\text{O}$, если известно, что его удельная энергия связи равна $7,9761$ МэВ/нуклон.</p>"
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            "text" => "<p><strong>Дано:</strong></p><p>Изотоп кислорода: $^{16}_8\text{O}$</p><p>Удельная энергия связи: $E_{уд} = 7,9761$ МэВ/нуклон</p><p><em>Справочные данные:</em></p><p>Масса протона: $m_p \approx 1,007276$ а.е.м.</p><p>Масса нейтрона: $m_n \approx 1,008665$ а.е.м.</p><p>1 атомная единица массы (а.е.м.) $\approx 1,66054 \cdot 10^{-27}$ кг.</p><p>Энергетический эквивалент 1 а.е.м.: $E_0 \approx 931,5$ МэВ/а.е.м.</p><p>1 МэВ = $1,60218 \cdot 10^{-13}$ Дж.</p><p><strong>Перевод в систему СИ:</strong></p><p>Хотя для решения задачи удобнее использовать внесистемные единицы (а.е.м. и МэВ), приведем значение удельной энергии связи в СИ (Джоуль/нуклон):</p><p>$E_{уд} = 7,9761 \frac{\text{МэВ}}{\text{нуклон}} = 7,9761 \cdot 1,60218 \cdot 10^{-13} \frac{\text{Дж}}{\text{нуклон}} \approx 1,2779 \cdot 10^{-12}$ Дж/нуклон.</p><p><strong>Найти:</strong></p><p>$m_я$ — масса ядра атома кислорода.</p><p><strong>Решение:</strong></p><p><strong>1.</strong> Сначала определим состав ядра атома кислорода $^{16}_8\text{O}$.</p><p>Массовое число $\text{A}$ (общее число нуклонов в ядре) равно 16.</p><p>Зарядовое число $\text{Z}$ (число протонов в ядре) равно 8.</p><p>Число нейтронов $\text{N}$ в ядре находим по формуле: $N = A - Z = 16 - 8 = 8$.</p><p>Таким образом, ядро кислорода-16 состоит из 8 протонов и 8 нейтронов.</p><p><strong>2.</strong> Рассчитаем полную энергию связи ядра ($E_{св}$). Она равна произведению удельной энергии связи на число нуклонов в ядре:</p><p>$E_{св} = E_{уд} \cdot A$</p><p>$E_{св} = 7,9761 \frac{\text{МэВ}}{\text{нуклон}} \cdot 16 \text{ нуклонов} = 127,6176$ МэВ.</p><p><strong>3.</strong> Энергия связи ядра соответствует дефекту масс ($\Delta m$) согласно формуле Эйнштейна $E = mc^2$. Дефект масс — это разница между суммарной массой свободных нуклонов, из которых состоит ядро, и реальной массой самого ядра. Выразим дефект масс в атомных единицах массы (а.е.м.):</p><p>$\Delta m = \frac{E_{св}}{E_0} = \frac{127,6176 \text{ МэВ}}{931,5 \text{ МэВ/а.е.м.}} \approx 0,1369915$ а.е.м.</p><p><strong>4.</strong> Теперь рассчитаем суммарную массу всех протонов и нейтронов, если бы они находились в свободном состоянии:</p><p>$m_{нуклонов} = Z \cdot m_p + N \cdot m_n$</p><p>$m_{нуклонов} = 8 \cdot 1,007276 \text{ а.е.м.} + 8 \cdot 1,008665 \text{ а.е.м.} = 8,058208 \text{ а.е.м.} + 8,069320 \text{ а.е.м.} = 16,127528$ а.е.м.</p><p><strong>5.</strong> Масса ядра ($m_я$) меньше суммарной массы его составляющих на величину дефекта масс:</p><p>$m_я = m_{нуклонов} - \Delta m$</p><p>$m_я = 16,127528 \text{ а.е.м.} - 0,1369915 \text{ а.е.м.} = 15,9905365$ а.е.м.</p><p>Округлим результат до шести знаков после запятой:</p><p>$m_я \approx 15,990537$ а.е.м.</p><p>При необходимости можно перевести это значение в систему СИ (килограммы):</p><p>$m_я \approx 15,990537 \text{ а.е.м.} \cdot 1,66054 \cdot 10^{-27} \frac{\text{кг}}{\text{а.е.м.}} \approx 2,6553 \cdot 10^{-26}$ кг.</p><p><strong>Ответ:</strong> масса ядра атома кислорода $^{16}_8\text{O}$ составляет приблизительно $15,990537$ а.е.м. (или $2,6553 \cdot 10^{-26}$ кг).</p>"
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            "text" => "<p><strong>Дано:</strong></p><p>Изотоп кислорода: $^{16}_8\text{O}$</p><p>Удельная энергия связи: $E_{уд} = 7,9761$ МэВ/нуклон</p><p><em>Справочные данные:</em></p><p>Масса протона: $m_p \approx 1,007276$ а.е.м.</p><p>Масса нейтрона: $m_n \approx 1,008665$ а.е.м.</p><p>1 атомная единица массы (а.е.м.) $\approx 1,66054 \cdot 10^{-27}$ кг.</p><p>Энергетический эквивалент 1 а.е.м.: $E_0 \approx 931,5$ МэВ/а.е.м.</p><p>1 МэВ = $1,60218 \cdot 10^{-13}$ Дж.</p><p><strong>Перевод в систему СИ:</strong></p><p>Хотя для решения задачи удобнее использовать внесистемные единицы (а.е.м. и МэВ), приведем значение удельной энергии связи в СИ (Джоуль/нуклон):</p><p>$E_{уд} = 7,9761 \frac{\text{МэВ}}{\text{нуклон}} = 7,9761 \cdot 1,60218 \cdot 10^{-13} \frac{\text{Дж}}{\text{нуклон}} \approx 1,2779 \cdot 10^{-12}$ Дж/нуклон.</p><p><strong>Найти:</strong></p><p>$m_я$ — масса ядра атома кислорода.</p><p><strong>Решение:</strong></p><p><strong>1.</strong> Сначала определим состав ядра атома кислорода $^{16}_8\text{O}$.</p><p>Массовое число $\text{A}$ (общее число нуклонов в ядре) равно 16.</p><p>Зарядовое число $\text{Z}$ (число протонов в ядре) равно 8.</p><p>Число нейтронов $\text{N}$ в ядре находим по формуле: $N = A - Z = 16 - 8 = 8$.</p><p>Таким образом, ядро кислорода-16 состоит из 8 протонов и 8 нейтронов.</p><p><strong>2.</strong> Рассчитаем полную энергию связи ядра ($E_{св}$). Она равна произведению удельной энергии связи на число нуклонов в ядре:</p><p>$E_{св} = E_{уд} \cdot A$</p><p>$E_{св} = 7,9761 \frac{\text{МэВ}}{\text{нуклон}} \cdot 16 \text{ нуклонов} = 127,6176$ МэВ.</p><p><strong>3.</strong> Энергия связи ядра соответствует дефекту масс ($\Delta m$) согласно формуле Эйнштейна $E = mc^2$. Дефект масс — это разница между суммарной массой свободных нуклонов, из которых состоит ядро, и реальной массой самого ядра. Выразим дефект масс в атомных единицах массы (а.е.м.):</p><p>$\Delta m = \frac{E_{св}}{E_0} = \frac{127,6176 \text{ МэВ}}{931,5 \text{ МэВ/а.е.м.}} \approx 0,1369915$ а.е.м.</p><p><strong>4.</strong> Теперь рассчитаем суммарную массу всех протонов и нейтронов, если бы они находились в свободном состоянии:</p><p>$m_{нуклонов} = Z \cdot m_p + N \cdot m_n$</p><p>$m_{нуклонов} = 8 \cdot 1,007276 \text{ а.е.м.} + 8 \cdot 1,008665 \text{ а.е.м.} = 8,058208 \text{ а.е.м.} + 8,069320 \text{ а.е.м.} = 16,127528$ а.е.м.</p><p><strong>5.</strong> Масса ядра ($m_я$) меньше суммарной массы его составляющих на величину дефекта масс:</p><p>$m_я = m_{нуклонов} - \Delta m$</p><p>$m_я = 16,127528 \text{ а.е.м.} - 0,1369915 \text{ а.е.м.} = 15,9905365$ а.е.м.</p><p>Округлим результат до шести знаков после запятой:</p><p>$m_я \approx 15,990537$ а.е.м.</p><p>При необходимости можно перевести это значение в систему СИ (килограммы):</p><p>$m_я \approx 15,990537 \text{ а.е.м.} \cdot 1,66054 \cdot 10^{-27} \frac{\text{кг}}{\text{а.е.м.}} \approx 2,6553 \cdot 10^{-26}$ кг.</p><p><strong>Ответ:</strong> масса ядра атома кислорода $^{16}_8\text{O}$ составляет приблизительно $15,990537$ а.е.м. (или $2,6553 \cdot 10^{-26}$ кг).</p>"
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№2 (с. 323)
Условие. №2 (с. 323)
скриншот условия
Физика, 9 класс Учебник, авторы: Грачев Александр Васильевич, Погожев Владимир Александрович, Боков Павел Юрьевич, издательство Вентана-граф, Москва, 2012, страница 323, номер 2, Условие

2. Определите массу ядра атома кислорода ${}_{8}^{16}\text{O}$, если известно, что его удельная энергия связи равна $7,9761$ МэВ/нуклон.

Решение. №2 (с. 323)

Дано:

Изотоп кислорода: $^{16}_8\text{O}$

Удельная энергия связи: $E_{уд} = 7,9761$ МэВ/нуклон

Справочные данные:

Масса протона: $m_p \approx 1,007276$ а.е.м.

Масса нейтрона: $m_n \approx 1,008665$ а.е.м.

1 атомная единица массы (а.е.м.) $\approx 1,66054 \cdot 10^{-27}$ кг.

Энергетический эквивалент 1 а.е.м.: $E_0 \approx 931,5$ МэВ/а.е.м.

1 МэВ = $1,60218 \cdot 10^{-13}$ Дж.

Перевод в систему СИ:

Хотя для решения задачи удобнее использовать внесистемные единицы (а.е.м. и МэВ), приведем значение удельной энергии связи в СИ (Джоуль/нуклон):

$E_{уд} = 7,9761 \frac{\text{МэВ}}{\text{нуклон}} = 7,9761 \cdot 1,60218 \cdot 10^{-13} \frac{\text{Дж}}{\text{нуклон}} \approx 1,2779 \cdot 10^{-12}$ Дж/нуклон.

Найти:

$m_я$ — масса ядра атома кислорода.

Решение:

1. Сначала определим состав ядра атома кислорода $^{16}_8\text{O}$.

Массовое число $\text{A}$ (общее число нуклонов в ядре) равно 16.

Зарядовое число $\text{Z}$ (число протонов в ядре) равно 8.

Число нейтронов $\text{N}$ в ядре находим по формуле: $N = A - Z = 16 - 8 = 8$.

Таким образом, ядро кислорода-16 состоит из 8 протонов и 8 нейтронов.

2. Рассчитаем полную энергию связи ядра ($E_{св}$). Она равна произведению удельной энергии связи на число нуклонов в ядре:

$E_{св} = E_{уд} \cdot A$

$E_{св} = 7,9761 \frac{\text{МэВ}}{\text{нуклон}} \cdot 16 \text{ нуклонов} = 127,6176$ МэВ.

3. Энергия связи ядра соответствует дефекту масс ($\Delta m$) согласно формуле Эйнштейна $E = mc^2$. Дефект масс — это разница между суммарной массой свободных нуклонов, из которых состоит ядро, и реальной массой самого ядра. Выразим дефект масс в атомных единицах массы (а.е.м.):

$\Delta m = \frac{E_{св}}{E_0} = \frac{127,6176 \text{ МэВ}}{931,5 \text{ МэВ/а.е.м.}} \approx 0,1369915$ а.е.м.

4. Теперь рассчитаем суммарную массу всех протонов и нейтронов, если бы они находились в свободном состоянии:

$m_{нуклонов} = Z \cdot m_p + N \cdot m_n$

$m_{нуклонов} = 8 \cdot 1,007276 \text{ а.е.м.} + 8 \cdot 1,008665 \text{ а.е.м.} = 8,058208 \text{ а.е.м.} + 8,069320 \text{ а.е.м.} = 16,127528$ а.е.м.

5. Масса ядра ($m_я$) меньше суммарной массы его составляющих на величину дефекта масс:

$m_я = m_{нуклонов} - \Delta m$

$m_я = 16,127528 \text{ а.е.м.} - 0,1369915 \text{ а.е.м.} = 15,9905365$ а.е.м.

Округлим результат до шести знаков после запятой:

$m_я \approx 15,990537$ а.е.м.

При необходимости можно перевести это значение в систему СИ (килограммы):

$m_я \approx 15,990537 \text{ а.е.м.} \cdot 1,66054 \cdot 10^{-27} \frac{\text{кг}}{\text{а.е.м.}} \approx 2,6553 \cdot 10^{-26}$ кг.

Ответ: масса ядра атома кислорода $^{16}_8\text{O}$ составляет приблизительно $15,990537$ а.е.м. (или $2,6553 \cdot 10^{-26}$ кг).

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