Question

The velocity of $e^{-}$ in a certain Bohr orbit of the hydrogen atom bears the ratio 1:275 to the velocity of light. The quantum no."$n$" of the orbit is:

• A. $2$
• B. $3$
• C. $4$
• D. $5$

Answer 1

Answer: (A)

$2$

Velocity in Bohr's orbit is given by
$mvr=n\frac{h}{2\pi }$
$\Rightarrow v=\frac{nh}{2\pi mr}$
Radius $r$ is given by
$r=0.53\times {10}^{-10}\times n^{2}m$
$\Rightarrow v=\frac{nh}{2\pi m\times 0.53\times {10}^{-10}\times n^2}$
$\Rightarrow v=\frac{h\times {10}^{10}}{1.06\pi nm}$
Ratio of this velocity with velocity of light
$\frac{v}{c}=\frac{1}{275}$
$\Rightarrow n=2$