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Консультация № 118062
12.01.2008, 00:38
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1
Помогите пожалуйста заочнику решить задачу,я запутался.
скорость электрона V=0,8*c (с-скорость света в вакууме).зная энергию покоя электрона в мегаэлектрон-вольтах,определить в тех же единицах кинетическую энергию электрона
скорость электрона V=0,8*c (с-скорость света в вакууме).зная энергию покоя электрона в мегаэлектрон-вольтах,определить в тех же единицах кинетическую энергию электрона
Обсуждение
Неизвестный
12.01.2008, 02:56
общий
это ответ
Здравствуйте, егорка!
Выпишем необходимые для решения задачи табличные данные:
m0 = 9,11*10^–31 кг –масса покоя электрона;
с = 3*10^8 м/с – скорость света;
1эВ = 1,602*10^–19 Дж;
β = v/c – отношение скорости движения релятивистской частицы к скорости света (для нашей задачи β = 0,8.
В релятивистской динамике кинетическая энергия частицы (в частности, электрона) вы-ражается уравнением: Екин = m0*c^2*((1/(√(1 – β^2)) – 1). (1)
Здесь Е0 = m0*c^2 – энергия покоя электрона. Вычислим ее в мегаэлектрон-вольтах:
Е0 = 9,11*10^–31*9*10^16 Дж = 82*10^–15 Дж/(1,602*10^–19) = 51,18*10^4 эВ =
= 0,5118*10^6 эВ = 0,5118 МэВ.
Подставляя это значение в (1) получим кинетическую энергию электрона, движущегося с релятивистской скоростью 0,8с: Екин = 0,5118*((1/(√(1 – 0,8^2)) – 1) = 0,5118*((1/0,6) –1)) =
= 0,5118*(10/6 – 1) = 0,5118*(1,6666 – 1) = 0,5118*0,6666 = 0,34 МэВ.
Ответ: Кинетическая энергия электрона, движущегося с релятивистской скоростью 0,8с равна 0,34 МэВ.
Выпишем необходимые для решения задачи табличные данные:
m0 = 9,11*10^–31 кг –масса покоя электрона;
с = 3*10^8 м/с – скорость света;
1эВ = 1,602*10^–19 Дж;
β = v/c – отношение скорости движения релятивистской частицы к скорости света (для нашей задачи β = 0,8.
В релятивистской динамике кинетическая энергия частицы (в частности, электрона) вы-ражается уравнением: Екин = m0*c^2*((1/(√(1 – β^2)) – 1). (1)
Здесь Е0 = m0*c^2 – энергия покоя электрона. Вычислим ее в мегаэлектрон-вольтах:
Е0 = 9,11*10^–31*9*10^16 Дж = 82*10^–15 Дж/(1,602*10^–19) = 51,18*10^4 эВ =
= 0,5118*10^6 эВ = 0,5118 МэВ.
Подставляя это значение в (1) получим кинетическую энергию электрона, движущегося с релятивистской скоростью 0,8с: Екин = 0,5118*((1/(√(1 – 0,8^2)) – 1) = 0,5118*((1/0,6) –1)) =
= 0,5118*(10/6 – 1) = 0,5118*(1,6666 – 1) = 0,5118*0,6666 = 0,34 МэВ.
Ответ: Кинетическая энергия электрона, движущегося с релятивистской скоростью 0,8с равна 0,34 МэВ.
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