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Консультация № 186000
10.05.2012, 19:52
101.51 руб.
10.05.2012, 21:33
0
1
1
Здравствуйте! У меня возникли сложности с таким вопросом:
1. Электрон находится в бесконечно глубокой одномерной потенциальной яме шириной 0,1 пм. Вычислить длину волны излучения при переходе электрона со второго на первый энергетический уровень.
1. Электрон находится в бесконечно глубокой одномерной потенциальной яме шириной 0,1 пм. Вычислить длину волны излучения при переходе электрона со второго на первый энергетический уровень.
Обсуждение
10.05.2012, 23:08
общий
это ответ
Здравствуйте, Екатерина!
Пусть стенки ямы находятся в точках 0 и l, соответственно. Примем потенциальную энергию на дне ямы нулевой. Стационарное уравнение Шрёдингера:
.
(Везде, где я пишу h, и не оговорено противное, подразумевается h-с-чертой; т.е. постоянная Планка, делённая на два пи)
Это уравнение гармонического осциллятора. Его решение имеет вид
. Т.к. яма бесконечная, на её краях волновая функция должна обращаться в ноль:
.
Первое уравнение даёт
.
А второе
,
откуда
.
Заметим, что n не должно быть равным нулю - волновая функция не может быть тождественно равной нулю. Так что, в последней формуле можно считать n=1,2,3,...
Энергия излучённого фотона
.
В последнем равенстве и до конца решения h - "нормальная h", т.е. постоянная Планка.
.
Откуда искомая длина волны
= 8/3 * 3*10^8 * ( 9.1 * 10^(-31) * (0.1 * 10^(-12))^2 ) / (1.1 * 10^(-34))
= 6.6 * 10^(-14) м = 66 фм.
Пусть стенки ямы находятся в точках 0 и l, соответственно. Примем потенциальную энергию на дне ямы нулевой. Стационарное уравнение Шрёдингера:
.(Везде, где я пишу h, и не оговорено противное, подразумевается h-с-чертой; т.е. постоянная Планка, делённая на два пи)
Это уравнение гармонического осциллятора. Его решение имеет вид
. Т.к. яма бесконечная, на её краях волновая функция должна обращаться в ноль:.Первое уравнение даёт
.А второе
,откуда
.Заметим, что n не должно быть равным нулю - волновая функция не может быть тождественно равной нулю. Так что, в последней формуле можно считать n=1,2,3,...
Энергия излучённого фотона
.В последнем равенстве и до конца решения h - "нормальная h", т.е. постоянная Планка.
.Откуда искомая длина волны
= 8/3 * 3*10^8 * ( 9.1 * 10^(-31) * (0.1 * 10^(-12))^2 ) / (1.1 * 10^(-34))= 6.6 * 10^(-14) м = 66 фм.
Форма ответа
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