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Q.36) A model for quantized motion of an electron in a uniform magnetic field $B$ states that the flux passing through the orbit of the electron is $n(h/ e)$ where $n$ is an integer, $h$ is Planck's constant and $e$ is the magnitude of electron's charge. According to the model, the magnetic moment of an electron in its lowest energy state will be ( $m$ is the mass of the electron)

A) $
\frac{h e B}{2 \pi m}
$

B) $
\frac{h e}{\pi m}
$

C) $
\frac{h e}{2\pi m}
$

D) $
\frac{h e B}{\pi m}
$

 

Answers (1)

best_answer

Magnetic moment is given as-

$\mu=I \cdot A= \frac{e v}{2 \pi r} \cdot \pi r^2=\frac{e v r}{2}$

From Lorentz force,

$\frac{m v^2}{r}=e v B \Rightarrow v=\frac{e B r}{m}$

So, $\mu = \frac{e^2}{2m }Br^2$

Also,

$B \pi r^2 = n(h/e)$

Then,

$\mu = \frac{e^2}{2m} \times \frac{nh}{\pi e}$
$\mu = \frac{he}{2 \pi m}$

Hence, the answer is the option 3.

Posted by

Saumya Singh

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