NEET 2025 — Physics solution

NEET2025Physics

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
$\frac{h e}{π m}$
B
$\frac{h e}{2 π m}$
C
$\frac{h e B}{π m}$
D
$\frac{h e B}{2 π m}$

Solution

Magnetic moment of a charged particle in circular orbit: $M = I A = (\frac{e v}{2 π r}) π r^{2} = \frac{e v r}{2}$ .

Flux quantization (lowest state $n = 1$ ): $B π r^{2} = h / e \Rightarrow r^{2} = \frac{h}{B π e}$ .

For circular motion in magnetic field, $r = \frac{m v}{e B} \Rightarrow v = \frac{e B r}{m}$ .

Substitute: $M = \frac{e \cdot r}{2} \cdot \frac{e B r}{m} = \frac{e ^{2} B r ^{2}}{2 m} = \frac{e ^{2} B}{2 m} \cdot \frac{h}{B π e} = \frac{e h}{2 π m}$ .

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