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Консультация № 200478
23.03.2021, 18:42
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Здравствуйте! У меня возникли сложности с таким вопросом:Пользуясь соотношением неопределённостей, оцените размеры атома, если электрон в нем движется со скоростью, отвечающей прохождению ускоряющего потенциала U= 1,38 * 10 (в пятой степени) В.
Обсуждение
24.03.2021, 08:54
общий
это ответ
Здравствуйте, mail!
Предлагаю Вам следующее решение задачи.
Дано:
В -- ускоряющий потенциал.
Определить:
-- линейный размер атома, в котором движется электрон под действием ускоряющего потенциала.
Вычислим энергию
покоя электрона:
(Дж)
(э*В).
Вычислим кинетическую энергию
электрона, прошедшего разность потенциалов В:
(Дж)
(э*В).
Поскольку и -- величины одного порядка, постольку в данном случае электрон является релятивистской частицей. Следовательно, его кинетическая энергия может быть вычислена по формуле
где
Тогда
то есть электрон движется со скоростью
Для неопределённостей
координаты и 
импульса электрона имеет место соотношение
где
Дж*с -- постоянная Планка.
Предположим, что -- линейный размер атома. Будем считать, что электрон находится в пределах области с неопределённостью 
Тогда
причём неопределённость импульса не больше его значения
то есть
Так как
(кг*м/с),
то
(м).
Ответ:
м.
Литература
Белонучкин В. Е., Заикин Д. А., Ципенюк Ю. М. Основы физики. Курс общей физики: Учебн. В 2 т. т. 2. Квантовая и статистическая физика / Под ред. Ю. М. Ципенюка. -- М.: ФИЗМАТЛИТ, 2001. -- 504 с.
Предлагаю Вам следующее решение задачи.
Дано:
В -- ускоряющий потенциал.Определить:
-- линейный размер атома, в котором движется электрон под действием ускоряющего потенциала.Решение
Вычислим энергию
покоя электрона: (Дж) (э*В).Вычислим кинетическую энергию
электрона, прошедшего разность потенциалов В: (Дж) (э*В).Поскольку
и -- величины одного порядка, постольку в данном случае электрон является релятивистской частицей. Следовательно, его кинетическая энергия может быть вычислена по формулегде
Тогдато есть электрон движется со скоростью
Для неопределённостей
координаты и импульса электрона имеет место соотношениегде
Дж*с -- постоянная Планка.Предположим, что
-- линейный размер атома. Будем считать, что электрон находится в пределах области с неопределённостью Тогдапричём неопределённость импульса не больше его значения
то естьТак как
(кг*м/с),то
(м).Ответ:
м.Литература
Белонучкин В. Е., Заикин Д. А., Ципенюк Ю. М. Основы физики. Курс общей физики: Учебн. В 2 т. т. 2. Квантовая и статистическая физика / Под ред. Ю. М. Ципенюка. -- М.: ФИЗМАТЛИТ, 2001. -- 504 с.
Об авторе:
Facta loquuntur.
Facta loquuntur.
Форма ответа
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