A stationary hydrogen atom of mass M emits a photon corresponding to the first line of Lyman series. If R is the Rydberg's constant, the velocity that the atom acquires is

Question

A stationary hydrogen atom of mass M emits a photon corresponding to the first line of Lyman series. If R is the Rydberg's constant, the velocity that the atom acquires is (A) (3/4) (R h/M) (B) (R h/4 M) (C) (R h/2 M) (D) (R h/M)

Tardigrade Admin · Accepted Answer

From conservation of momentum: M V=(h/λ)=h R(1-(1/4)) ⇒ V=(3/4) (h R/M)

Q. A stationary hydrogen atom of mass $M$ emits a photon corresponding to the first line of Lyman series. If $R$ is the Rydberg's constant, the velocity that the atom acquires is

$\frac{3}{4} \frac{R h}{M}$

$\frac{R h}{4 M}$

$\frac{R h}{2 M}$

$\frac{R h}{M}$

From conservation of momentum:
$M V = \frac{h}{λ} = h R (1 - \frac{1}{4})$
$\Rightarrow V = \frac{3}{4} \frac{h R}{M}$

Q. A stationary hydrogen atom of mass M emits a photon corresponding to the first line of Lyman series. If R is the Rydberg's constant, the velocity that the atom acquires is

43​MRh​

4MRh​

2MRh​

MRh​