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Номер 7.13, страница 39 - гдз по физике 9 класс задачник Артеменков, Ломаченков
Авторы: Артеменков Д. А., Ломаченков И. А., Панебратцев Ю. А.
Тип: Задачник
Серия: сферы
Издательство: Просвещение
Год издания: 2011 - 2026
Цвет обложки: синий
ISBN: 978-5-09-038216-8
Популярные ГДЗ в 9 классе
VII. Квантовые явления - номер 7.13, страница 39.
App\Models\Task {#1003 // 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" => 1424304 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_page_start" => "39" "field_page_end" => null "field_url" => "/9-klass/fizika/artemenkov-zadachnik/7-13" "field_display_title" => "7.13" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1009 #items: array:1 [ 0 => App\Models\Term {#1008 #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 00:54:11" "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 00:54:11" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1007 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1046 #items: array:1 [ 0 => App\Models\Branch {#1006 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:23 [ "id" => 1424070 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_display_title" => "VII. 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"id" => 2549 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1013 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1015 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1017 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1019 #items: array:3 [ …3] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1023 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1024 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1026 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1028 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1030 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1032 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1033 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1034 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => "2" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1035 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1037 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2011" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное пособие для общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "278" "field_priority" => null "field_default_folder" => "/fizika_09/artemenkov-z/" "field_isbn" => "978-5-09-038216-8" "field_cover" => array:1 [ 0 => "/media/fizika_09/artemenkov-z/covers/cover1.webp" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ …4] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1038 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1039 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1040 #items: [] #escapeWhenCastingToString: false } "field_url" => "/9-klass/fizika/artemenkov-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1041 #items: array:1 [ …1] #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" => 2549 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1013} "field_class" => Illuminate\Database\Eloquent\Collection {#1015} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1017} "field_author" => Illuminate\Database\Eloquent\Collection {#1019} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1023} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1024} "field_country" => Illuminate\Database\Eloquent\Collection {#1026} "field_city" => Illuminate\Database\Eloquent\Collection {#1028} "field_series" => Illuminate\Database\Eloquent\Collection {#1030} "field_umk" => Illuminate\Database\Eloquent\Collection {#1032} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1033} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1034} "field_publication_number" => "2" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1035} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1037} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2011" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное пособие для общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "278" "field_priority" => null "field_default_folder" => "/fizika_09/artemenkov-z/" "field_isbn" => "978-5-09-038216-8" "field_cover" => array:1 [ 0 => "/media/fizika_09/artemenkov-z/covers/cover1.webp" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ …4] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1038} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1039} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1040} "field_url" => "/9-klass/fizika/artemenkov-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1041} "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 {#1043 #items: [] #escapeWhenCastingToString: false } ] #original: array:23 [ "id" => 1424070 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_display_title" => "VII. Квантовые явления" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1011} "field_page_start" => "38" "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" => [] "book" => Illuminate\Database\Eloquent\Collection {#1010} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1043} ] #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 {#1044 #items: array:1 [ 0 => App\Models\Branch {#1006} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1047 #items: array:2 [ 0 => App\Models\Element {#1056 #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" => 1673922 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1065 #items: array:1 [ 0 => App\Models\Edition {#1057 #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" => 5990 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1059 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1060 #items: [] …1 } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1061 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1062 …2} "field_content_source" => null ] #original: array:21 [ "id" => 5990 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1059} "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 {#1060 …1} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1061 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1062 …2} "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" => "1424304" "type" => "task" ] "text" => "<p><strong>7.13</strong> Определите наибольшую длину волны в ультрафиолетовом спектре водорода.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "13-1.jpg" "alt" => null "width" => "1724" "height" => 216 "path" => "/media/fizika_09/artemenkov-z/0-7/13-1.webp?ts=1758726431" ] ] ] #original: array:7 [ "id" => 1673922 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1065} "task" => array:2 [ "refs" => "1424304" "type" => "task" ] "text" => "<p><strong>7.13</strong> Определите наибольшую длину волны в ультрафиолетовом спектре водорода.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "13-1.jpg" "alt" => null "width" => "1724" "height" => 216 "path" => "/media/fizika_09/artemenkov-z/0-7/13-1.webp?ts=1758726431" ] ] ] #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 {#1063 #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" => 1695464 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1073 #items: array:1 [ 0 => App\Models\Edition {#1064 #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" => 6166 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1067 …2} "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 {#1068 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1069 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1070 …2} "field_content_source" => null ] #original: array:21 [ "id" => 6166 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1067 …2} "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 {#1068 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1069 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1070 …2} "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" => "1424304" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Ультрафиолетовый спектр водорода (серия Лаймана)</p><p>Постоянная Ридберга $R \approx 1,097 \cdot 10^7 \text{ м}^{-1}$</p><p><strong>Найти:</strong></p><p>$\lambda_{max}$ - ?</p><p><strong>Решение:</strong></p><p>Спектральные линии в ультрафиолетовой области спектра водорода образуют серию Лаймана. Эта серия возникает при переходах электронов с высших энергетических уровней на первый (основное состояние), то есть $n_1 = 1$.</p><p>Длина волны излучаемого фотона определяется обобщенной формулой Бальмера (формулой Ридберга):</p><p>$\frac{1}{\lambda} = R \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right)$</p><p>где $n_1$ — номер уровня, на который происходит переход, а $n_2$ — номер уровня, с которого происходит переход ($n_2 > n_1$).</p><p>Наибольшая длина волны $\lambda_{max}$ соответствует наименьшей энергии фотона $\Delta E_{min}$, а следовательно, переходу электрона между ближайшими возможными уровнями. Для серии Лаймана ($n_1=1$) таким переходом является переход с уровня $n_2=2$.</p><p>Подставим значения $n_1=1$ и $n_2=2$ в формулу Ридберга:</p><p>$\frac{1}{\lambda_{max}} = R \left( \frac{1}{1^2} - \frac{1}{2^2} \right) = R \left( 1 - \frac{1}{4} \right) = \frac{3}{4}R$</p><p>Отсюда выразим наибольшую длину волны:</p><p>$\lambda_{max} = \frac{4}{3R}$</p><p>Подставим числовое значение постоянной Ридберга:</p><p>$\lambda_{max} = \frac{4}{3 \cdot 1,097 \cdot 10^7 \text{ м}^{-1}} \approx 1,215 \cdot 10^{-7} \text{ м}$</p><p>Переведем результат в нанометры: $1,215 \cdot 10^{-7} \text{ м} = 121,5 \text{ нм}$.</p><p><strong>Ответ:</strong> Наибольшая длина волны в ультрафиолетовом спектре водорода составляет приблизительно $121,5 \text{ нм}$.</p>" ] #original: array:6 [ "id" => 1695464 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1073} "task" => array:2 [ "refs" => "1424304" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Ультрафиолетовый спектр водорода (серия Лаймана)</p><p>Постоянная Ридберга $R \approx 1,097 \cdot 10^7 \text{ м}^{-1}$</p><p><strong>Найти:</strong></p><p>$\lambda_{max}$ - ?</p><p><strong>Решение:</strong></p><p>Спектральные линии в ультрафиолетовой области спектра водорода образуют серию Лаймана. Эта серия возникает при переходах электронов с высших энергетических уровней на первый (основное состояние), то есть $n_1 = 1$.</p><p>Длина волны излучаемого фотона определяется обобщенной формулой Бальмера (формулой Ридберга):</p><p>$\frac{1}{\lambda} = R \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right)$</p><p>где $n_1$ — номер уровня, на который происходит переход, а $n_2$ — номер уровня, с которого происходит переход ($n_2 > n_1$).</p><p>Наибольшая длина волны $\lambda_{max}$ соответствует наименьшей энергии фотона $\Delta E_{min}$, а следовательно, переходу электрона между ближайшими возможными уровнями. Для серии Лаймана ($n_1=1$) таким переходом является переход с уровня $n_2=2$.</p><p>Подставим значения $n_1=1$ и $n_2=2$ в формулу Ридберга:</p><p>$\frac{1}{\lambda_{max}} = R \left( \frac{1}{1^2} - \frac{1}{2^2} \right) = R \left( 1 - \frac{1}{4} \right) = \frac{3}{4}R$</p><p>Отсюда выразим наибольшую длину волны:</p><p>$\lambda_{max} = \frac{4}{3R}$</p><p>Подставим числовое значение постоянной Ридберга:</p><p>$\lambda_{max} = \frac{4}{3 \cdot 1,097 \cdot 10^7 \text{ м}^{-1}} \approx 1,215 \cdot 10^{-7} \text{ м}$</p><p>Переведем результат в нанометры: $1,215 \cdot 10^{-7} \text{ м} = 121,5 \text{ нм}$.</p><p><strong>Ответ:</strong> Наибольшая длина волны в ультрафиолетовом спектре водорода составляет приблизительно $121,5 \text{ нм}$.</p>" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] 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Illuminate\Database\Eloquent\Collection {#1045} "field_class" => Illuminate\Database\Eloquent\Collection {#1055} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1049} "field_author" => Illuminate\Database\Eloquent\Collection {#1050} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1075} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1076} "field_country" => Illuminate\Database\Eloquent\Collection {#1078} "field_city" => Illuminate\Database\Eloquent\Collection {#1080} "field_series" => Illuminate\Database\Eloquent\Collection {#1082} "field_umk" => Illuminate\Database\Eloquent\Collection {#1084} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1085} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1086} "field_publication_number" => "2" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1087} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1089} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2011" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное пособие для общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "278" "field_priority" => null "field_default_folder" => "/fizika_09/artemenkov-z/" "field_isbn" => "978-5-09-038216-8" "field_cover" => array:1 [ 0 => "/media/fizika_09/artemenkov-z/covers/cover1.webp" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_09/artemenkov-z/covers/cover1.webp" "alt" => "" "width" => "1888" "height" => "2427" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1090} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1091} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1092} "field_url" => "/9-klass/fizika/artemenkov-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1093} "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 } "page" => Illuminate\Database\Eloquent\Collection {#1316 #items: array:1 [ 0 => App\Models\BookPage {#1004 #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" => 1424389 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_page_start" => "39" "field_url" => "/9-klass/fizika/artemenkov-zadachnik/page-39" "field_display_title" => "39" "field_folder" => "1" "field_image_name" => "39" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#313 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#304 #items: array:1 [ 0 => App\Models\Book {#1095 #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" => 2549 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1096 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1099 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1101 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1103 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1107 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1108 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1110 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1112 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1114 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1116 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1117 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1118 …2} "field_publication_number" => "2" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1119 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1121 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2011" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное пособие для общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "278" "field_priority" => null "field_default_folder" => "/fizika_09/artemenkov-z/" "field_isbn" => "978-5-09-038216-8" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1122 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1123 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1124 …2} "field_url" => "/9-klass/fizika/artemenkov-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1125 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #original: array:50 [ "id" => 2549 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1096 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1099 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1101 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1103 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1107 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1108 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1110 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1112 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1114 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1116 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1117 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1118 …2} "field_publication_number" => "2" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1119 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1121 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2011" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное пособие для общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "278" "field_priority" => null "field_default_folder" => "/fizika_09/artemenkov-z/" "field_isbn" => "978-5-09-038216-8" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1122 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1123 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1124 …2} "field_url" => "/9-klass/fizika/artemenkov-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1125 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #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 "edition_groups" => Illuminate\Database\Eloquent\Collection {#1127 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1128 #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" => 1674199 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1130 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #original: array:6 [ "id" => 1674199 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1130 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #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" => "1424390" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1424388" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1137 #items: array:10 [ 0 => App\Models\Task {#1138 #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" => 1424302 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_page_start" => "39" "field_page_end" => null "field_url" => "/9-klass/fizika/artemenkov-zadachnik/7-11" "field_display_title" => "7.11" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1139 …2} "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 {#1141 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1142 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1178 …2} "content" => Illuminate\Database\Eloquent\Collection {#1179 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1196 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1424302 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_page_start" => "39" "field_page_end" => null "field_url" => "/9-klass/fizika/artemenkov-zadachnik/7-11" "field_display_title" => "7.11" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1139 …2} "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 {#1141 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1142 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1178 …2} "content" => Illuminate\Database\Eloquent\Collection {#1179 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1196 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Task {#1197 #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" => 1424303 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_page_start" => "39" "field_page_end" => null "field_url" => "/9-klass/fizika/artemenkov-zadachnik/7-12" "field_display_title" => "7.12" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1198 …2} "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 {#1199 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1200 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1201 …2} "content" => Illuminate\Database\Eloquent\Collection {#1202 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1219 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1424303 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_page_start" => "39" "field_page_end" => null "field_url" => "/9-klass/fizika/artemenkov-zadachnik/7-12" "field_display_title" => "7.12" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1198 …2} "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 {#1199 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1200 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1201 …2} "content" => Illuminate\Database\Eloquent\Collection {#1202 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1219 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Task {#1220 #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" => 1424304 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_page_start" => "39" "field_page_end" => null "field_url" => "/9-klass/fizika/artemenkov-zadachnik/7-13" "field_display_title" => "7.13" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1221 …2} "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 {#1222 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1223 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1224 …2} "content" => Illuminate\Database\Eloquent\Collection {#1225 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1236 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1424304 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_page_start" => "39" "field_page_end" => null "field_url" => "/9-klass/fizika/artemenkov-zadachnik/7-13" "field_display_title" => "7.13" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1221 …2} "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 {#1222 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1223 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1224 …2} "content" => Illuminate\Database\Eloquent\Collection {#1225 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1236 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 3 => App\Models\Task {#1237 #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" => 1424305 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_page_start" => "39" "field_page_end" => null "field_url" => "/9-klass/fizika/artemenkov-zadachnik/7-14" "field_display_title" => "7.14" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1238 …2} "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 {#1239 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1240 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1241 …2} "content" => Illuminate\Database\Eloquent\Collection {#1242 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1247 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1424305 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_page_start" => "39" "field_page_end" => null "field_url" => "/9-klass/fizika/artemenkov-zadachnik/7-14" "field_display_title" => "7.14" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1238 …2} "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 {#1239 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1240 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1241 …2} "content" => Illuminate\Database\Eloquent\Collection {#1242 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1247 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 4 => App\Models\Task {#1248 #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" => 1424306 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_page_start" => "39" "field_page_end" => null "field_url" => "/9-klass/fizika/artemenkov-zadachnik/7-15" "field_display_title" => "7.15" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1249 …2} "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 {#1250 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1251 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1252 …2} "content" => Illuminate\Database\Eloquent\Collection {#1253 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1258 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1424306 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_page_start" => "39" "field_page_end" => null "field_url" => "/9-klass/fizika/artemenkov-zadachnik/7-15" "field_display_title" => "7.15" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1249 …2} "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 {#1250 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1251 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1252 …2} "content" => Illuminate\Database\Eloquent\Collection {#1253 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1258 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 5 => App\Models\Task {#1259 #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" => 1424307 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_page_start" => "39" "field_page_end" => null "field_url" => "/9-klass/fizika/artemenkov-zadachnik/7-16" "field_display_title" => "7.16" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1260 …2} "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 {#1261 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1262 …2} "parent_branches" => 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{#1263 …2} "content" => Illuminate\Database\Eloquent\Collection {#1264 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1269 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 6 => App\Models\Task {#1270 #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" => 1424308 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_page_start" => "39" "field_page_end" => null "field_url" => "/9-klass/fizika/artemenkov-zadachnik/7-17" "field_display_title" => "7.17" 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#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" => 1424309 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_page_start" => "39" "field_page_end" => null "field_url" => "/9-klass/fizika/artemenkov-zadachnik/7-18" "field_display_title" => "7.18" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1282 …2} "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 {#1283 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1284 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1285 …2} "content" => Illuminate\Database\Eloquent\Collection {#1286 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1291 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1424309 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_page_start" => "39" "field_page_end" => null "field_url" => "/9-klass/fizika/artemenkov-zadachnik/7-18" "field_display_title" => "7.18" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1282 …2} "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 {#1283 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1284 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1285 …2} "content" => Illuminate\Database\Eloquent\Collection 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№7.13 (с. 39)
Условие. №7.13 (с. 39)
скриншот условия
7.13 Определите наибольшую длину волны в ультрафиолетовом спектре водорода.
Решение. №7.13 (с. 39)
Дано:
Ультрафиолетовый спектр водорода (серия Лаймана)
Постоянная Ридберга $R \approx 1,097 \cdot 10^7 \text{ м}^{-1}$
Найти:
$\lambda_{max}$ - ?
Решение:
Спектральные линии в ультрафиолетовой области спектра водорода образуют серию Лаймана. Эта серия возникает при переходах электронов с высших энергетических уровней на первый (основное состояние), то есть $n_1 = 1$.
Длина волны излучаемого фотона определяется обобщенной формулой Бальмера (формулой Ридберга):
$\frac{1}{\lambda} = R \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right)$
где $n_1$ — номер уровня, на который происходит переход, а $n_2$ — номер уровня, с которого происходит переход ($n_2 > n_1$).
Наибольшая длина волны $\lambda_{max}$ соответствует наименьшей энергии фотона $\Delta E_{min}$, а следовательно, переходу электрона между ближайшими возможными уровнями. Для серии Лаймана ($n_1=1$) таким переходом является переход с уровня $n_2=2$.
Подставим значения $n_1=1$ и $n_2=2$ в формулу Ридберга:
$\frac{1}{\lambda_{max}} = R \left( \frac{1}{1^2} - \frac{1}{2^2} \right) = R \left( 1 - \frac{1}{4} \right) = \frac{3}{4}R$
Отсюда выразим наибольшую длину волны:
$\lambda_{max} = \frac{4}{3R}$
Подставим числовое значение постоянной Ридберга:
$\lambda_{max} = \frac{4}{3 \cdot 1,097 \cdot 10^7 \text{ м}^{-1}} \approx 1,215 \cdot 10^{-7} \text{ м}$
Переведем результат в нанометры: $1,215 \cdot 10^{-7} \text{ м} = 121,5 \text{ нм}$.
Ответ: Наибольшая длина волны в ультрафиолетовом спектре водорода составляет приблизительно $121,5 \text{ нм}$.
Другие задания:
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