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Добрый день. Помогите решить задачку (срочно, горю..): Энергия Ферми при абсолютном нуле для натрия равна 3,15 эВ. Найти число свободных электронов, приходящихся на один атом натрия. Отблагодарю 60 рублей (переведу на Ваш кошелек rfpro.ru).
Рассчитаем объём, приходящийся на атом натрия: плотность [$961$]=0,971 г/см3 молярная масса M=23 г/моль 1 моль натрия занимает объём Vm=M/[$961$]=23,7 см3/моль=2,37*10-5 м3/моль 1 атом занимает объём V=Vm/NA=3,94*10-29 м3
ħ=1,055*10-34 Дж*с масса электрона m=9,11*10-31 кг Энергия ферми Ef=5.046*10-19 Дж
выражаем количество электронов N=V/(3π2)*(Ef*2m/ħ2)1,5=0,9977≈1 Что и требовалось доказать
5
Большое спасибо!
Неизвестный
04.06.2009, 17:54
общий
Не совсем понял. У Вас в ответе:
выражаем количество электронов N=V/(3π2)*(Ef*2m/ħ2)1,5=0,9977≈1
Т.е. 1 свободный электрон приходится на один атом натрия? И что Вы хотите сказать словами:
Т.е. 1 свободный электрон приходится на один атом натрия?
Именно это. В атоме натрия на внешнем уровне находится 1 электрон, который настолько слабо связан с ядром, что в металле является практически свободным. Остальные 10 электронов находятся наболее глубоких уровнях и прочно связаны с ядром. Для кальция, например, искомое значение близко к 2, а для алюминия - к 3.
Неизвестный
05.06.2009, 09:22
общий
Химик CH: Спасибо. Все понятно.
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