Question

The radius of the orbit of a hydrogen atom is 0.85nm. The velocity of an electron in this orbit is:

• A. $5.44\times {10}^5$m/s
• B. $5.62\times {10}^5$m/s
• C. $5.48\times {10}^5$m/s
• D. $5.67\times {10}^5$m/s

Answer 1

Answer: (A)

$5.44\times {10}^5$m/s

For $H$-atom radius is given by
$r=\frac{n^2{h}^2}{4{\pi }^{2}mk{e}^2}$
where $k=\frac{1}{4\pi {ϵ}_o}=9\times {10}^{9}N{m}^2{C}^{-2}$
$r=0.85nm=8.5\times {10}^{-10}m$
$r=\frac{n^2{h}^2}{4{\pi }^{2}mk{e}^2}=8.5\times {10}^{-10}$
$\Rightarrow r=0.53\times {10}^{-10}\times n^2=8.5\times {10}^{-10}$
$\Rightarrow n=4$
Velocity is given by
$mvr=n\frac{h}{2\pi }$
$\Rightarrow v=4\times \frac{\frac{6.62\times {10}^{-34}}{2\pi }}{9.1096\times {10}^{-31}\times 8.5\times {10}^{-10}}$
$\Rightarrow v=5.44\times {10}^{5}mse{c}^{-1}$