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Консультация № 173564
22.10.2009, 19:13
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Здравствуйте, помогите пожалуста решить:
Фотон с энергией 0,51 МэВ при рассеянии на свободном электроне потерял половину своей энергии. Определить угол рассеяния.
Спасибо большое)
Фотон с энергией 0,51 МэВ при рассеянии на свободном электроне потерял половину своей энергии. Определить угол рассеяния.
Спасибо большое)
Обсуждение
25.10.2009, 19:18
общий
это ответ
Здравствуйте, Kvaliks.
Используя законы сохранения импульса и энергии, а также теорему косинусов, можно показать, что импульсы фотона до и после рассеяния (pф и p’ф соответственно) связаны соотношением
p’ф = mcpф/(mc + pф(1 – cos θ)),
тогда
mc + pф(1 – cos θ) = mcpф/p’ф,
pф(1 – cos θ) = mcpф/p’ф – mc,
1 – cos θ = mc/p’ф – mc/pф,
cos θ = mc/pф – mc/p’ф + 1, (1)
где m – масса покоя электрона.
Поскольку pф = Wф/c, p’ф = W’ф/c, то выражение (1) преобразовывается:
cos θ = mc2/Wф – mc2/W’ф + 1 = mc2(1/Wф – 2/Wф) + 1 = -mc2/Wф + 1, (2)
и после подстановки в формулу (2) числовых значений величин получаем
cos θ = -9,11 ∙ 10-31 ∙ (3,00 ∙ 108)2/(8,16 ∙ 10-14) + 1 ≈ 0,90.
Следовательно, искомый угол рассеяния равен θ = arccos 0,90 ≈ 26°.
Ответ: 26°.
С уважением.
Используя законы сохранения импульса и энергии, а также теорему косинусов, можно показать, что импульсы фотона до и после рассеяния (pф и p’ф соответственно) связаны соотношением
p’ф = mcpф/(mc + pф(1 – cos θ)),
тогда
mc + pф(1 – cos θ) = mcpф/p’ф,
pф(1 – cos θ) = mcpф/p’ф – mc,
1 – cos θ = mc/p’ф – mc/pф,
cos θ = mc/pф – mc/p’ф + 1, (1)
где m – масса покоя электрона.
Поскольку pф = Wф/c, p’ф = W’ф/c, то выражение (1) преобразовывается:
cos θ = mc2/Wф – mc2/W’ф + 1 = mc2(1/Wф – 2/Wф) + 1 = -mc2/Wф + 1, (2)
и после подстановки в формулу (2) числовых значений величин получаем
cos θ = -9,11 ∙ 10-31 ∙ (3,00 ∙ 108)2/(8,16 ∙ 10-14) + 1 ≈ 0,90.
Следовательно, искомый угол рассеяния равен θ = arccos 0,90 ≈ 26°.
Ответ: 26°.
С уважением.
Об авторе:
Facta loquuntur.
Facta loquuntur.
Форма ответа
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