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Консультация № 197343
07.12.2019, 21:56
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
При какой скорости v импульс электрона р совпадет по модулю с импульсом фотона, длина волны которого L = 0,001 нм.
При какой скорости v импульс электрона р совпадет по модулю с импульсом фотона, длина волны которого L = 0,001 нм.
Обсуждение
12.12.2019, 04:43
общий
это ответ
Здравствуйте, оксана!
Импульс частицы массы m, движущейся со скоростью v, равен
импульс же фотона (не имеющего массы покоя и движущегося со скоростью света) определяется как
где [$955$] - длина волны, h = 6.6261[$183$]10[sup]-34[/sup] Дж[$183$]с - постоянная Планка. Приравнивая, получаем
откуда
В данном случае [$955$] = 0.001 нм = 10[sup]-12[/sup] м, m = 9.1086[$183$]10[sup]-31[/sup] кг - масса электрона, и для его скорости получаем
м/с.
Данный результат более чем в два раза превышает значение скорости света c [$8776$] 2.998[$183$]10[sup]8[/sup] м/с, что физически невозможно. Следовательно, нужно рассматривать электрон как релятивистскую частицу, импульс которой определяется выражением
Тогда из
следует
где v[sub]0[/sub] - полученное ранее значение скорости нерелятивистского электрона. Следовательно,
м/с
- "правильное" значение скорости электрона (с учётом релятивистских эффектов).
Импульс частицы массы m, движущейся со скоростью v, равен
импульс же фотона (не имеющего массы покоя и движущегося со скоростью света) определяется как
где [$955$] - длина волны, h = 6.6261[$183$]10[sup]-34[/sup] Дж[$183$]с - постоянная Планка. Приравнивая, получаем
откуда
В данном случае [$955$] = 0.001 нм = 10[sup]-12[/sup] м, m = 9.1086[$183$]10[sup]-31[/sup] кг - масса электрона, и для его скорости получаем
м/с.Данный результат более чем в два раза превышает значение скорости света c [$8776$] 2.998[$183$]10[sup]8[/sup] м/с, что физически невозможно. Следовательно, нужно рассматривать электрон как релятивистскую частицу, импульс которой определяется выражением
Тогда из
следует
где v[sub]0[/sub] - полученное ранее значение скорости нерелятивистского электрона. Следовательно,
м/с- "правильное" значение скорости электрона (с учётом релятивистских эффектов).
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