The electron of an H -atom is revolving around the nucleus in circular orbit having radius (h^2)/(4 π m e^2) with ((2 π e^2)/(h)) . The current produced due to the motion of electron is

Correct answer: D. (4 π^2 m e^5)/(h^3) As we know that time period, T=(2 π r)/(V) aligned T & =2 π × (h^2)/(4 π m e^2) × (h)/(2 π e^2) & =(h^3)/(4 π^2 m e^4) aligned aligned Current, i & = Charge (q) T & =(e)/(T)=(e)/((h^3)/(4 π^2 m e^4)) & =(4 π^2 m e^5)/(h^3) aligned

JIPMER 2015

Exam: JIPMER
Year: 2015
Subject: Physics
Chapter: Atomic Physics

JIPMER 2015 · Physics · Atomic Physics

The electron of an H -atom is revolving around the nucleus in...

The electron of an H -atom is revolving around the nucleus in circular orbit having radius

\frac{h^2}{4 \pi m e^2}

with \left(\frac{2 \pi e^2}{h}\right)$. The current produced due to the motion of electron is

Options

A $\frac{2 \pi m^2 e^2}{3 h^2}$
Bzero
C $\frac{2 \pi^2 m e}{h^2}$
D $\frac{4 \pi^2 m e^5}{h^3}$

Correct answer

D. $\frac{4 \pi^2 m e^5}{h^3}$

Step-by-step solution

As we know that time period,

T=\frac{2 \pi r}{V}

\begin{aligned} \therefore \quad T & =2 \pi \times \frac{h^2}{4 \pi m e^2} \times \frac{h}{2 \pi e^2} \\ & =\frac{h^3}{4 \pi^2 m e^4}\end{aligned}

\begin{aligned} \therefore \quad \text{ Current, } i & =\frac{\text{ Charge }(q)}{T} \\ & =\frac{e}{T}=\frac{e}{\frac{h^3}{4 \pi^2 m e^4}} \\ & =\frac{4 \pi^2 m e^5}{h^3}\end{aligned}

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