Question

An electron in the hydrogen atom is revolving around a
proton with a speed of $\frac{e^2}{h}$ . The radiys of the electron orbit is equal to $\frac{h^2}{m{e}^2}$ . Obtain the formula for the electric current in the above case. Mass of the electron $=m,$charge on electron $=e.$(Hint :$h=\frac{h}{2\pi })$

Answer 1

Speed of electron is $=\frac{e^2}{k}$ and radius of orbit $=\frac{{\hslash }^2}{m{e}^2}$

So , time period of revolution is $=T=\frac{2\pi r}{v}$

$\Rightarrow T=\frac{2\pi \times \frac{{\hslash }^2}{m{e}^2}}{e^2/h}=\frac{\pi h{\hslash }^2}{m}=\frac{h^3}{2\pi m}[\hslash =\frac{h}{2\pi }]$

$\therefore$ Current due to revolution, $I=\frac{charge}{time}=\frac{e}{t}=\frac{2\pi me}{h^3}$