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.

Answer 1

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 n^th orbit. 

f = `"v"/(2pi"r")= (4pi^2"mk"^2"e"^4)/("n"^3"h"^3)`