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Консультация № 185663
25.03.2012, 16:50
66.20 руб.
0
2
2
Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Оцените с помощью соотношения неопределённостей Гейзенберга неопределённость скорости электрона в атоме водорода, полагая размер атома a=10-10м.Сравните полученную величину со скоростью электрона на первой боровской орбите.
Заранее благодарен за помощь!
Оцените с помощью соотношения неопределённостей Гейзенберга неопределённость скорости электрона в атоме водорода, полагая размер атома a=10-10м.Сравните полученную величину со скоростью электрона на первой боровской орбите.
Заранее благодарен за помощь!
Обсуждение
25.03.2012, 17:10
общий
это ответ
Здравствуйте, G-buck!
Скорость электрона на первой боровской орбите вычисляется, например, здесь как 2,183*106 м/с
Соотношение Гейзенберга можно записать как
[$8710$]x [$8710$]v > h/m
где [$8710$]x=10-10 м
h( приведенная постоянная Планка)=1,054 x 10–34 Дж·с
m(масса электрона) =9,1*10-31 кг
Значит [$8710$]v >1,054 x 10–34 /(9,1*10-31*10-10)=1,16*106м/c
Таким образом, неопределенность скорости электрона сравнима по порядку величины со скоростью электрона.
Скорость электрона на первой боровской орбите вычисляется, например, здесь как 2,183*106 м/с
Соотношение Гейзенберга можно записать как
[$8710$]x [$8710$]v > h/m
где [$8710$]x=10-10 м
h( приведенная постоянная Планка)=1,054 x 10–34 Дж·с
m(масса электрона) =9,1*10-31 кг
Значит [$8710$]v >1,054 x 10–34 /(9,1*10-31*10-10)=1,16*106м/c
Таким образом, неопределенность скорости электрона сравнима по порядку величины со скоростью электрона.
5
Неизвестный
26.03.2012, 16:20
общий
это ответ
Здравствуйте, G-buck!
Согласно соотношению неопределённостей:
v = ħ/(ma) = 1,054*10^(-34)/[10^(-10)*9,1*10^(-31)] = 1,1*10^6 м/с
Скорость электрона на 1-ой Боровской орбите:
v = ħ/(mr) = 1,054*10^(-34)/[5,29*10^(-11)*9,1*10^(-31)] = 2,18*10^6 м/с
r - радиус 1-ой Боровской орбиты.
Согласно соотношению неопределённостей:
v = ħ/(ma) = 1,054*10^(-34)/[10^(-10)*9,1*10^(-31)] = 1,1*10^6 м/с
Скорость электрона на 1-ой Боровской орбите:
v = ħ/(mr) = 1,054*10^(-34)/[5,29*10^(-11)*9,1*10^(-31)] = 2,18*10^6 м/с
r - радиус 1-ой Боровской орбиты.
5
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