Question

An electron revolving in an orbit of radius $0.5\mathring{A}$ in a hydrogen atom executes $10$ revolutions per second. The magnetic moment of electron due to its orbital motion will be :

• A. $1256\times {10}^{-41}A{m}^2$
• B. $653\times {10}^{-41}A{m}^2$
• C. $0$
• D. $256\times {10}^{-41}A{m}^2$

Answer 1

The correct option is A $1256\times {10}^{-41}A{m}^2$

Radius of orbit $=0.5A^{\circ }$
$I=\frac{Charge}{Time}=\frac{10\times 1.6\times {10}^{-19}}{1}=1.6\times {10}^{-18}$
Magnetic moment $=I\pi r^2$
$=1.6\times {10}^{-18}\times \pi \times (0.5\times {10}^{-10}{)}^2$
$=1256.63\times {10}^{-(38+3)}=1256\times {10}^{-41}A{m}^2$