The electron of H - atom is revolving around the nucleus in circular orbit having radius $\frac{h^{2}}{4 π {me}^{2}}$ with $(\frac{2 π e^{2}}{h})$ . The current produced due to the motion of electron is

$\frac{2 π m^{2} e^{2}}{3 h^{2}}$

zero

$\frac{2 π^{2} me}{h^{2}}$

$\frac{4 π^{2} {me}^{5}}{h^{3}}$

Solution

$\frac{4 π^{2} {me}^{5}}{h^{3}}$

Given:-

radius r = $\frac{h^{2}}{4 πm e^{2}}$

velocity v = $\frac{2 {πe}^{2}}{h}$

As we know that time period

T = $\frac{2 π r}{v}$

∴ T = $2 π \times \frac{h^{2}}{4 {πme}^{2}} \times \frac{h}{2 {πe}^{2}}$

= $\frac{h^{3}}{4 π^{2} m e^{4}}$

∴ Current i = $\frac{Charge (q)}{T}$

= $\frac{e}{T}$

curent i = $\frac{e}{\frac{h^{3}}{4 πm e^{4}}}$

i = $\frac{4 π^{2} m e^{5}}{h^{3}}$

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