An electron in the ground state of hydrogen was excited to a higher energy level using monochromatic radiations of wave length `(lambda )975 Å` . The longest wave length that appears in the resulting spectrum is due to transition from:

Options

A. `n_(4) to n_(1)`
B. `n_(4) to n_(3)`
C. `n_(5) to n_(4)`
D. `n_(5) to n_(1)`

Answer

B

Explanation

The energy assoicated with radiation of wave length `975 Å` is given by
`E = (12400)/(975)eV = 12.72 eV`
[For a radiaton of wavelenght x `Å`
we know `E = (12400)/(x) eV`]
`E = 13.6 [(1)/(n_(1)^(2)) - (1)/(n_(2)^(2))]eV`
` or 12.72 = 13.6 [1 - (1)/(n_(2)^(2))] " "[because E = 12.72 eV]`
or ` (1)/(n_(2)^(2))k = (13.6-12.72)/(13.6) = (0.88)/(13.6) = (1)/(16)`
or `n_(2)^(2) = 16 , n_(2) ~= 4`
The transition `n_(4) to n_(3)` will give the longest wave lenght.