Question

If an electron is moving around nucleus of charge $2e$ in a circular orbit of radius ${10}^{-10}$ m, then the initial frequency of light emitted by the electron is

• A. $0.42\times {10}^{15}Hz$
• B. $0.36\times {10}^{15}Hz$
• C. $3.6\times {10}^{15}Hz$
• D. $4.2\times {10}^{15}Hz$

Answer 1

The correct option is C $3.6\times {10}^{15}Hz$

From $\frac{m{v}^2}{r}=\frac{kZ{e}^2}{r^2}$ we get $v=\sqrt{\frac{k{e}^{2}Z}{mr}}$

Frequency $\nu =\frac{v}{2\pi r}=\sqrt{\frac{k{e}^2}{4{\pi }^{2}m}}\frac{\sqrt{Z}}{r^{1.5}}$

$⟹$ $\nu =2.53\frac{\sqrt{Z}}{r^{1.5}}$

Given : $Z=2$ $r={10}^{-10}$m

$\therefore$ $\nu =2.53\times \frac{\sqrt{2}}{{10}^{-15}}=3.6\times {10}^{15}$ Hz