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Question
Derive an expression for the frequency of radiation emitted when a hydrogen atom de-excites from level n to level (n – 1). Also show that for large values of n, this frequency equals to classical frequency of revolution of an electron.
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Solution
From Bohr’s theory, the frequency f of the radiation emitted when an electron de-excites from level n2 to level n1 is given as -
`"f" = (2pi^2"mk"^2"z"^2"e"^4)/"h"^3[1/"n"_1^2 - 1/"n"_2^2]`
Given n1 = n − 1, n2 = n, derivation of it
`"f" = (2pi^2"mk"^2"z"^2"e"^4)/"h"^3 ((2"n" - 1))/(("n" - 1)^2"n"^2)`
For large n, 2n − 1 = 2n, n − 1 = n and z = 1
Thus,
f = `(4pi^2"mk"^2"e"^4)/("n"^3"h"^3)`
which is same as orbital frequency of electron in nth orbit.
f = `"v"/(2pi"r")= (4pi^2"mk"^2"e"^4)/("n"^3"h"^3)`
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