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Консультация № 196730
20.10.2019, 06:01
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Определите неопределенность ∆x в определении коорди-
наты электрона, движущегося в атоме со скоростью
v = 1,5 Мм/с, если неопределенность в определении скорости
составляет ∆v = 0,1v.
Определите неопределенность ∆x в определении коорди-
наты электрона, движущегося в атоме со скоростью
v = 1,5 Мм/с, если неопределенность в определении скорости
составляет ∆v = 0,1v.
Обсуждение
23.10.2019, 14:10
общий
это ответ
Здравствуйте, kuznarskaavalentina!
Дано: v=1,5*106 м/с -- скорость электрона; [$916$]v=0,1v -- неопределённость скорости электрона.
Определить: [$916$]x -- неопределённость координаты электрона.
Решение
Согласно [1, с. 744], при движении частицы в направлении оси x справедливо соотношение неопределённостей [$916$]x*[$916$]px[$8805$]h/2, где [$916$]px -- неопределённость импульса частицы по оси x, h[$8776$]1.05*10-34 Дж*с -- постоянная Планка [1, с. 1004]. Приняв, что [$916$]px=[$916$]p=m*[$916$]v, где m[$8776$]9,11*10-31 кг -- масса электрона [1, с. 1005], получим [$916$]x*m*[$916$]v[$8805$]h/2, откуда
Ответ: не менее 3,84*10-10 м.
Литература
1. Яворский Б. М., Детлаф А. А., Лебедев А. К. Справочник по физике для инженеров и студентов вузов. -- М.: ООО "Издательство Оникс", 2007. -- 1056 с.
Дано: v=1,5*106 м/с -- скорость электрона; [$916$]v=0,1v -- неопределённость скорости электрона.
Определить: [$916$]x -- неопределённость координаты электрона.
Решение
Согласно [1, с. 744], при движении частицы в направлении оси x справедливо соотношение неопределённостей [$916$]x*[$916$]px[$8805$]h/2, где [$916$]px -- неопределённость импульса частицы по оси x, h[$8776$]1.05*10-34 Дж*с -- постоянная Планка [1, с. 1004]. Приняв, что [$916$]px=[$916$]p=m*[$916$]v, где m[$8776$]9,11*10-31 кг -- масса электрона [1, с. 1005], получим [$916$]x*m*[$916$]v[$8805$]h/2, откуда
[$916$]x[$8805$]h/(2*m*[$916$]v)=h/(0,2mv)=1.05*10-34/(0,2*9,11*10-31*1,5*106)[$8776$]3,84*10-10 (м).
Ответ: не менее 3,84*10-10 м.
Литература
1. Яворский Б. М., Детлаф А. А., Лебедев А. К. Справочник по физике для инженеров и студентов вузов. -- М.: ООО "Издательство Оникс", 2007. -- 1056 с.
5
Об авторе:
Facta loquuntur.
Facta loquuntur.
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