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Консультация № 194074
02.12.2018, 22:28
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Уважаемые эксперты! Пожалуйста, помогите решить задачу:
Пользуясь соотношением неопределенностей, оцените размеры атома, если электрон в нем движется со скоростью, отвечающей прохождению ускоряющего потенциала U = 1,38*105 В.
Вот мое решение:
V=sqrt(2*e*U/m)=0.69*10^10 - скорость электрона по зак. сохранения эн.
Del x * Del px ~ h
представим Del x как 2*pi*r, Del px как p, а h как постоянную планка h
r*p~h
а дальше не знаю что делать
Пользуясь соотношением неопределенностей, оцените размеры атома, если электрон в нем движется со скоростью, отвечающей прохождению ускоряющего потенциала U = 1,38*105 В.
Вот мое решение:
V=sqrt(2*e*U/m)=0.69*10^10 - скорость электрона по зак. сохранения эн.
Del x * Del px ~ h
представим Del x как 2*pi*r, Del px как p, а h как постоянную планка h
r*p~h
а дальше не знаю что делать
Обсуждение
06.12.2018, 09:51
общий
это ответ
Здравствуйте, Durachok!
Вычислим энергию
покоя электрона:
(Дж)
(э*В).
Вычислим кинетическую энергию
электрона, прошедшего разность потенциалов 
В:
(Дж)
(э*В).
Поскольку и -- величины одного порядка, постольку в данном случае электрон является релятивистской частицей. Следовательно, его кинетическая энергия может быть вычислена по формуле
где
Тогда
то есть электрон движется со скоростью
Для неопределённостей
координаты и 
импульса электрона имеет место соотношение
где
Дж*с -- постоянная Планка.
Предположим, что
-- линейный размер атома. Будем считать, что электрон находится в пределах области с неопределённостью 
Тогда
причём неопределённость импульса не больше его значения
то есть
Так как
(кг*м/с),
то
(м).
Вычислим энергию
покоя электрона: (Дж) (э*В).Вычислим кинетическую энергию
электрона, прошедшего разность потенциалов В: (Дж) (э*В).Поскольку
и -- величины одного порядка, постольку в данном случае электрон является релятивистской частицей. Следовательно, его кинетическая энергия может быть вычислена по формулегде
Тогдато есть электрон движется со скоростью
Для неопределённостей
координаты и импульса электрона имеет место соотношениегде
Дж*с -- постоянная Планка.Предположим, что
-- линейный размер атома. Будем считать, что электрон находится в пределах области с неопределённостью Тогдапричём неопределённость импульса не больше его значения
то естьТак как
(кг*м/с),то
(м).
5
Доступно и понятно
Об авторе:
Facta loquuntur.
Facta loquuntur.
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