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. `(3Rh)/(4M)`
B. `(4M)/(3Rh)`
C. `(Rh)/(4M)`
D. `(4M)/(Rh)`

Answer

A

Explanation

`(1)/(lambda) = R((1 - (1)/(4)) = (3R)/(4)`
`:. P =(h)/(lambda)`
`=(3Rh)/(4) = momentum of photon`
From conservation of linear momentum,
Momentum of photon = Momentum of hydrogen atom
`: (3Rh)/(4) = Mv rArr v = (3Rh)/(4M).`