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Консультация № 194843
01.03.2019, 19:59
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Здравствуйте! У меня возникли сложности с таким вопросом:
Разница в длинах волн между головными линиями серии
Лаймана и Бальмера в спектре атомарного водорода составляет
Δλ=5347 Å. Вычислить значение постоянной Планка, считая массу
электрона, его заряд и скорость света известными.
Разница в длинах волн между головными линиями серии
Лаймана и Бальмера в спектре атомарного водорода составляет
Δλ=5347 Å. Вычислить значение постоянной Планка, считая массу
электрона, его заряд и скорость света известными.
Обсуждение
04.03.2019, 03:15
общий
это ответ
Здравствуйте, lenocvol!
Частота линии при переходе с уровня m на уровень n (n<m) определяется формулой Бальмера-Ридберга:
где R - постоянная Ридберга. В частности, для серии Лаймана n=1, для серии Бальмера n=2, для головной линии серии m=n+1, следовательно частота головных линий серии Лаймана и Бальмера будет равна:
Так как частота и длина волны связаны соотношением
где c = 2.9979[$183$]10[sup]8[/sup] м/с - скорость света, то длина волн головных линий серии Лаймана и Бальмера будет равна:
и разница между ними составит
откуда
С другой стороны, для постоянной Ридберга существует выражение
где m[sub]e[/sub] = 9.1086[$183$]10[sup]-31[/sup] кг - масса электрона, e = 1.6022[$183$]10[sup]-19[/sup] Кл - заряд электрона, [$949$][sub]0[/sub] = 8.8542[$183$]10[sup]-12[/sup] Ф/м - электрическая постоянная, h - постоянная Планка. Приравнивая, получаем
откуда
Дж[$183$]с, что близко к известному значению.
Частота линии при переходе с уровня m на уровень n (n<m) определяется формулой Бальмера-Ридберга:
где R - постоянная Ридберга. В частности, для серии Лаймана n=1, для серии Бальмера n=2, для головной линии серии m=n+1, следовательно частота головных линий серии Лаймана и Бальмера будет равна:
Так как частота и длина волны связаны соотношением
где c = 2.9979[$183$]10[sup]8[/sup] м/с - скорость света, то длина волн головных линий серии Лаймана и Бальмера будет равна:
и разница между ними составит
откуда
С другой стороны, для постоянной Ридберга существует выражение
где m[sub]e[/sub] = 9.1086[$183$]10[sup]-31[/sup] кг - масса электрона, e = 1.6022[$183$]10[sup]-19[/sup] Кл - заряд электрона, [$949$][sub]0[/sub] = 8.8542[$183$]10[sup]-12[/sup] Ф/м - электрическая постоянная, h - постоянная Планка. Приравнивая, получаем
откуда
Дж[$183$]с, что близко к известному значению.
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