Question

Calculate the velocity $\left(cm/sec\right)$ of an electron placed in the third orbit of the hydrogen atom. Also calculate the number of revolutions per second that this electron makes around the nucleus.

Answer 1

Radius of $3$rd orbit $=3^2\times 0.529\times {10}^{-8}=4.761\times {10}^{-8}cm$
We know that,
$mvr=\frac{nh}{2\pi }$ or $v=\frac{nh}{2\pi mr}$
$=\frac{3\times 6.624\times {10}^{-27}}{2\times 3.14\times (9.108\times {10}^{-28})\times (4.761\times {10}^{-8})}$
$=0.729\times {10}^{8}cm/sec$
Time taken for one revolution $=\frac{2\pi r}{v}$
Number of revolutions per second $=\frac{1}{\frac{2\pi r}{v}}=\frac{v}{2\pi r}$
$=\frac{0.729\times {10}^8}{2\times 3.14\times 4.761\times {10}^{-8}}$
$=2.4\times {10}^{14}revolutions/sec$.