An electrons of a stationary hydrogen atom passes form the fifth energy 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 constant and `h`, Planck's constant)

Options

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

Answer

B

Explanation

For the transition between `n_1=1` and `n_2=5`
`1/lambda=R(1/1-1/25)=(24R)/25`
`lambda=25/(24R)`
`p=h/lambda=(hxx24R)/25 =(24Rh)/25`
`mv=(24Rh)/25`
{Momentum of atom must be equal and opposite to momentum of photon , as per conservation of momentum}
`v=(24Rh)/(25m)`