An electrons of a stationary hydrogen aton passes form the fifth enegry level to the ground level. The velocity that the atom acquired as a result of photon emission will be
`(m` is the mass of the electron, `R`, Rydberg constanrt and `h`, Planck's constant)

Options

A. `(24hR)/(25m)`
B. `(25hR)/(25m)`
C. `(25m)/(24hR)`
D. `(24m)/(25hR)`

Answer

A

Explanation

For fifth energy level, `n_(2)=5` and for ground level, `n_(1)=1`. The wavelength `lambda` of radiation emitted is given by
`1/lambda=RZ^(2)(1/(n_(1)^(2))-1/(n_(2)^(2))) = Rxx1^(2)(1/(1^(2))-1/(5^(2)))=(24R)/25`
Linear momentum of photon emitted
`p=h/lambda=hxx(24R)/25`
As hydrogen atom is stationary, therefore, momentum acquired by electron as a result of photon emission =`mv=p=(24hR)/25`
`v=(24hR)/(25m)`