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Консультация № 196950
04.11.2019, 12:19
0.00 руб.
05.11.2019, 07:25
0
1
1
Здравствуйте! У меня возникли сложности с таким вопросом:
Используя выражение для удельной электрической проводимости металлов согласно квантовой теории, оцените величину <l>, играющую роль среднего свободного пробега электрона, для серебра (по оценке эта величина составляет сотни межузельных расстояний в решетке). Считать известными: заряд электрона |qe| = 1,6[$183$]10-19 Кл; массу электрона me = 9,1[$183$]10-31 кг; скорость электрона, находящегося на верхнем занятом энергетическом уровне для серебра U0 = 1,4[$183$]106 м/с; плотность электронного газа n = 1028 м-3; удельное сопротивление серебра (при t = 20°С) r = 1,6[$183$]10-8 Ом[$183$]м.
Используя выражение для удельной электрической проводимости металлов согласно квантовой теории, оцените величину <l>, играющую роль среднего свободного пробега электрона, для серебра (по оценке эта величина составляет сотни межузельных расстояний в решетке). Считать известными: заряд электрона |qe| = 1,6[$183$]10-19 Кл; массу электрона me = 9,1[$183$]10-31 кг; скорость электрона, находящегося на верхнем занятом энергетическом уровне для серебра U0 = 1,4[$183$]106 м/с; плотность электронного газа n = 1028 м-3; удельное сопротивление серебра (при t = 20°С) r = 1,6[$183$]10-8 Ом[$183$]м.
Обсуждение
09.11.2019, 07:20
общий
это ответ
Здравствуйте, haidarova.an!
В квантовой теории металлов удельная электрическая проводимость описывается выражением
где e, m[sub]e[/sub] и n - заряд, масса и концентрация электронов проводимости, <l[sub]F[/sub]> и <v[sub]F[/sub]> - средняя длина свободного пробега и средняя скорость электрона, имеющего энергию Ферми. Отсюда для <l[sub]F[/sub]> имеем
или, с учётом того, что [$947$] = 1/[$961$],
Подставляя исходные данные, получаем длину свободного пробега
м
или порядка 311 ангстрем. С учётом того, что межузельное расстояние для кристаллической решётки серебра равно примерно 4 ангстремам, полученная оценка составляет примерно 75-80 межузельных расстояний.
В квантовой теории металлов удельная электрическая проводимость описывается выражением
где e, m[sub]e[/sub] и n - заряд, масса и концентрация электронов проводимости, <l[sub]F[/sub]> и <v[sub]F[/sub]> - средняя длина свободного пробега и средняя скорость электрона, имеющего энергию Ферми. Отсюда для <l[sub]F[/sub]> имеем
или, с учётом того, что [$947$] = 1/[$961$],
Подставляя исходные данные, получаем длину свободного пробега
мили порядка 311 ангстрем. С учётом того, что межузельное расстояние для кристаллической решётки серебра равно примерно 4 ангстремам, полученная оценка составляет примерно 75-80 межузельных расстояний.
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