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Консультация № 176786

20.02.2010, 07:31

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Образование

Определить импульс p_e электрона отдачи, если фотон с энергией [$958$]₁=1,53 МэВ в результате рассеяния на свободном электроне потерял 1/3 своей энергии.

Обсуждение

давно

Roman Chaplinsky / Химик CH

Модератор
156417
2175

20.02.2010, 15:58

общий

это ответ

Здравствуйте, Lybares.
Очевидно, что энергия, потеряная фотоном, могля перейти лишь в кинетическую энергию электрона. Таким образом, электрон получает энергию E_k=0.51 МэВ.
Но энергия покоя электрона также равна m₀c²=0,51 МэВ, следовательно требуется использовать формулы релятивистской механики.
полная энергия E=m₀c²+E_k=m₀c²/[$8730$](1-v²/c²)
Учитывая, что по условию E_k=m₀c², получаем
2m₀c²=m₀c²/[$8730$](1-v²/c²)
1/[$8730$](1-v²/c²)=2
[$8730$](1-v²/c²)=1/2
1-v²/c²=1/4
v²/c²=3/4
v/c=0,5[$8730$]3
v=c*0,5[$8730$]3=0,866c
Импульс рассчитывается по формуле
p=m₀v/[$8730$](1-v²/c²)=2m₀v=m₀c[$8730$]3=1,732m₀c
подставляя значения, получаем 4.73*10^-22кг*м/с или 0,833 МэВ/c (в последней величине c не секунда, а скорость света)

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