A stationary hydrogen atom emits photon corresponding to the first line of Lyman series. If R is the Rydberg constant and M is the mass of the atom, then the velocity acquired by the atom is

Options

A. `(3)/(4) (R h)/(M)`
B. `(R h)/(4 M)`
C. `(R h)/(2 M)`
D. `(R h)/(M)`

Answer

A

Explanation

From conservation of momentum:
`M V = (h)/(lambda) = h R (1 - 1/(4)) implies V = (3)/(4) (h R)/(M)`