An electron of a stationary hydrogen atom (mass = m ) jumps from...

An electron of a stationary hydrogen atom (mass =

m

) jumps from the fifth energy level to the ground level. As a result, the atom emits a photon and recoils with some velocity. The velocity that the atom acquires as a result of photon emission is [h

= Planck's constant,

\text{ and } = Rydberg's constant]

Options

A $\dfrac{24hR}{25m}$
B $\dfrac{25hR}{24m}$
C $\dfrac{24m}{25hR}$
D $\dfrac{25m}{24hR}$

Correct answer

A. $\dfrac{24hR}{25m}$

Step-by-step solution

Here,

{E}_{5} - {E}_{1} = \dfrac{hc}{λ}

- ( \dfrac{Rhc}{52} - Rhc ) = \dfrac{hc}{λ}

(where

R =

Rydberg's constant,

h =

Planck's constant and

c =

speed of light in vacuum)

⇒ \dfrac{24}{25}R = \dfrac{1}{λ}

But

P = \dfrac{h}{λ}

⇒ v = \dfrac{h}{mλ} = \dfrac{24Rh}{25m}

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