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Консультация № 142470

28.08.2008, 09:50

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Образование

Альфа-частица находится в бесконечно глубоком, одномерном, прямоугольном потенциальном ящике. Используя соотношение неопределенностей, оценить ширину ящика, если известно, что минимальная энергия a-частицы Emin=8МэВ.

Обсуждение

Неизвестный

30.08.2008, 17:20

общий

это ответ

Здравствуйте, Doctorche!
Принцип неопределнности гласит, что произведение неопределённости импульса
[$916$]p и неопределённости координаты [$916$]х частицы примерно равно постоянной Планка h=1,0546*10^-34 Дж*с:
[$916$]p*[$916$]х=h (1)
В то же время неопределённость координаты [$916$]х и есть оцениваемая ширина потенциального ящика а. Связь импульса p с энергией E :
[$945$]-частицы:
p=[$8730$](2*m*E) (2)
где m= 6,645*10^-27 кг- масса [$945$]-частицы; неопределённость энергии это и есть минимальная энергия Emin=8 МэВ=5*10^-14 Дж
Тогда подставляя (2) в (1) выражаем ширину ящика а:
а=[$916$]х=h/[$8730$](2*m*E)=1,0546*10^-34/[$8730$](2*6,645*10^-27*5*10^-14)=0,256*10^-18 м

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