Question

If an electron revolves around a proton, then its time period $T$ is ($R=$ radius of orbit)-

• A. $\propto R^2$
• B. $\propto R^{\frac{3}{2}}$
• C. $\propto R^3$
• D. $\propto R$

Answer 1

The correct option is B $\propto R^{\frac{3}{2}}$

Electron revolves around a proton.
Let, $e=$ charge of the electtron.
and same $e=$ charge of the proton.
Now, as time period is given by $T=\frac{2\pi R}{v}$...(i)
where $R=$ radius of the circular orbit
$v=$ speed of the electron
$\because$ electron revolves around the proton,
therefore centripetal force $\left(F_c\right)$ will be balnaced by electrostatic force $\left(F_e\right)$.
$\therefore \frac{m{v}^2}{R}=\frac{ke\times e}{R^2}$
$v=\sqrt{\frac{e^{2}k}{mR}}....\left(ii\right)$
From equation (i) and (ii)
$T=\frac{2\pi }{\sqrt{e^{2}K}}\sqrt{m}{R}^{\frac{3}{2}}$
$T\propto R^{\frac{3}{2}}$