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Консультация № 198344
23.04.2020, 12:16
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Здравствуйте! Прошу помощи в следующем вопросе:
Определить импульс электрона отдачи, если фотон с энергией е= 1,53 МэВ в результате рассеяния на свободном электроне потерял 1/3 своей энергии.
Определить импульс электрона отдачи, если фотон с энергией е= 1,53 МэВ в результате рассеяния на свободном электроне потерял 1/3 своей энергии.
Обсуждение
28.04.2020, 04:21
общий
это ответ
Здравствуйте, Ульяна!
Изменение длины волны фотона при комптоновском рассеивании определяется формулой Комптона:
где m = 9.11[$183$]10[sup]-31[/sup] кг - масса электрона, h - постоянная Планка, c = 2.998[$183$]10[sup]8[/sup] м/с - скорость света, [$952$] - угол рассеяния фотона. Так как энергия фотона связана с частотой [$957$] и длиной волны [$955$] формулой Планка
то
При уменьшении энергии фотона E на 1/3, то есть до величины 2/3 E изменение длины волны фотона составит
Из равенства
получаем
Импульс фотона связан с его энергией соотношением
то есть до рассеяния импульс фотона был равен p[sub]1[/sub] = E/c, а после рассеивания (с учётом потери 1/3 энергии) - p[sub]2[/sub] = 2E/3c. Если выбрать направление движения фотона до рассеяния за ось Ox, то вектор импульса фотона будет равен
до рассеяния и
после рассеяния. Согласно закону сохранения импульса,
где p[sub]e[/sub] - импульс электрона отдачи. Отсюда
и
Подставляя найденное ранее значение
получаем
В данном случае для фотона с энергией E = 1.53 МэВ = 2.448[$183$]10[sup]-13[/sup] Дж импульс электрона отдачи будет равен
кг[$183$]м/с.
Изменение длины волны фотона при комптоновском рассеивании определяется формулой Комптона:
где m = 9.11[$183$]10[sup]-31[/sup] кг - масса электрона, h - постоянная Планка, c = 2.998[$183$]10[sup]8[/sup] м/с - скорость света, [$952$] - угол рассеяния фотона. Так как энергия фотона связана с частотой [$957$] и длиной волны [$955$] формулой Планка
то
При уменьшении энергии фотона E на 1/3, то есть до величины 2/3 E изменение длины волны фотона составит
Из равенства
получаем
Импульс фотона связан с его энергией соотношением
то есть до рассеяния импульс фотона был равен p[sub]1[/sub] = E/c, а после рассеивания (с учётом потери 1/3 энергии) - p[sub]2[/sub] = 2E/3c. Если выбрать направление движения фотона до рассеяния за ось Ox, то вектор импульса фотона будет равен
до рассеяния и
после рассеяния. Согласно закону сохранения импульса,
где p[sub]e[/sub] - импульс электрона отдачи. Отсюда
и
Подставляя найденное ранее значение
получаем
В данном случае для фотона с энергией E = 1.53 МэВ = 2.448[$183$]10[sup]-13[/sup] Дж импульс электрона отдачи будет равен
кг[$183$]м/с.
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