Question

If in the H-atom, the electron is moving with velocity v in an orbit of radius r, then the equivalent magnetic moment will be:-

• A. ${\mu }_{0}e/2r$
• B. $ev/r^2$
• C. $ev\times {10}^{-}7/r^3$
• D. $evr/2$

Answer 1

Answer: (D)

$evr/2$

Given: velocity =v, radius =r

Solution: The electron is moving with velocity v in an orbit of radius r ,time period is given by:

$T=\frac{2\pi r}{v}$

And as we know that $i=\frac{q}{t}$

$i=\frac{ev}{2\pi r}$

formula of magnetic moment (M)=iA

$M=\frac{ev}{2\pi r}\times \pi r^2=\frac{evr}{2}$

Hence the correct answer is D