Question

An electron in a circular orbit of radius $0.05nm$ performs ${10}^{16}$ revolutions per second. The magnetic moment due to this rotation of electron is (in ${Am}^2$):

• A. $2.16\times {10}^{-23}$
• B. $3.21\times {10}^{-22}$
• C. $3.21\times {10}^{-24}$
• D. $1.26\times {10}^{-23}$

Answer 1

The correct option is D $1.26\times {10}^{-23}$

Given : $\nu ={10}^{16}$ rev. per sec

$r=0.05$ $nm=5\times {10}^{-11}$ $m$

Area of the circular orbit $A=\pi r^2=3.14\times (5\times {10}^{-11}{)}^2=7.85\times {10}^{-21}$ $m^2$

Magnetic moment $\mu =IA$ where $I=e\nu$

$⟹$ $\mu =e\nu A=1.6\times {10}^{-19}\times {10}^{16}\times 7.85\times {10}^{-21}$

$\mu =1.26\times {10}^{-23}$ $A{m}^2$