If the wavelength of photon emitted due to transition of electron from third orbit to first orbit in a hydrogen atom is `lambda` then the wavelength of photon emitted due to transition of electron from fourth orbit to second orbit will be

Options

A. `(128)/(27) lambda`
B. `(25)/(9) lambda`
C. `(36)/(7) lambda`
D. `(125)/(11) lambda`

Answer

A

Explanation

`(1)/(lambda) = R [(1)/(2^(2)) - (1)/(4^(2))] implies lambda = (9)/(8 R)`
Again `(1)/(lambda') = R [(1)/(1^(2)) - (1)/(3^(2))] implies lambda' = (16)/(3 R)`
Now, `(lambda')/(lambda) = (16)/(3 R) xx (8 R)/(9) or lambda = (128)/(27) lambda`