Question

In the Bohr model an electron moves in a circular orbit around the proton. Considering the orbiting electron to be circular current loop, the magnetic moment of the hydrogen atom, when 5th electron is in $n^{th}$ excited state, is:

• A. $\left(\frac{e}{2m}\right)\frac{{\pi }^{2}h}{2}$
• B. $\left(\frac{e}{m}\right)\frac{n^{}h}{2\pi }$
• C. $\left(\frac{e}{2m}\right)\frac{n^{}h}{2\pi }$
• D. $\left(\frac{e}{m}\right)\frac{n^{2}h}{2\pi }$

Answer 1

The correct option is C $\left(\frac{e}{2m}\right)\frac{n^{}h}{2\pi }$

$\mu =iA$

maguehic moment

$\begin{array}{cc}\mu & =\frac{q}{T}\times \pi r^2\\ & =\frac{e}{T}x-\pi r^2\\ \mu & =\frac{e\pi r^2}{T}-\left(I\right)\end{array}$

we know, frum bohs wodel

$\begin{array}{cc}r& =\frac{n^2{h}^2}{4{\pi }^2{m}^{}{e}^2}\\ T& =\frac{4{\epsilon }_0^2{h}^3}{m{e}^4}{n}^3\end{array}$

putting in $VI$

$\mu =\frac{\mathrm{enh}}{2m\times 2\pi }$

$CorrectC$