Question

An electron of a stationary hydrogen atom passes from the fifth energy level to the ground level. The velocity that the atom acquired as a result of photon emission will be
($m$ is the mass of the electron, $R$, Rydberg constant and $h$ Planck's constant).

• A. $\frac{24hR}{25m}$
• B. $\frac{25hR}{24m}$
• C. $\frac{25m}{24hR}$
• D. $\frac{24m}{25hR}$

Answer 1

The correct option is A $\frac{24hR}{25m}$

Here, $E_5-E_1=\frac{hc}{\lambda }$

and

$\frac{Rhc}{25}=Rhc=\frac{hc}{\lambda }$

$\frac{24}{25}R=\frac{1}{\lambda }$ ......................(1)

We have,

$P=\frac{h}{\lambda }$

Where $P$ is momemtum

Also, $P=mv$

Where $m$ is mass and $v$ is velocity

$mv=\frac{h}{\lambda }$

$v=\frac{h}{m\lambda }$ .........................(2)

Substituting the value of $\frac{1}{\lambda }$ from equation (1) in equation (2), we get

$v=\frac{24hR}{25m}$