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

`13.6 z^(2) ((1)/(1^(2))-(1)/(3^(2))) =(hc)/(lambda)`
`13.6z^(2) ((1)/(2^(2))-(1)/(4^(2))) = (hc)/(lambda_(1))`
On division, `((8)/(9))/((3)/(16)) = (lambda_(1))/(lambda)`
`:. lambda_(1) = (128)/(27)lambda`