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

(a) 3Rh/4M

(b) 4M/3Rh

(c) Rh/4M

(d) 4M/Rh

Ans: (a)

Sol: For first Line of Lyman series ,

1/λ = R[1/1^{2} − 1/2^{2}] = R[1 −1/4] = 3R/4

Momentum P = h/λ

⇒ Mv = h/λ = h(3R/4)

hence , v = 3Rh/4M