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)/(1^(2)) -(1)/(3^(2))]`
`(1)/(lambda) = R[1-(1)/(9)] = (8R)/(9)` or `lambda = (9)/(8)R`
Again, `(1)/(lambda) = R[(1)/(2^(2)) -(1)/(4^(2))]`
or `(1)/(lambda') = R[(1)/(4) -(1)/(16)]`or `(1)/(lambda') = R xx(3)/(16)`
or `lambda' = (16)/(3)R`
`(lambda')/(lambda') = (16)/(3R) xx (8R)/(9)`
or `lambda' = (128)/(127)lambda`.