An electron revolving in $\mathrm{n}^{\text {th }}$ Bohr orbit has magnetic moment $\mu_{n}$. If $\mu_{n} \alpha n^{x}$, the value of $x$ is:

JEE Main · 2024 · 30 Jan 2024 · Shift 2 · Modern Physics

An electron revolving in

n^{th}

Bohr orbit has magnetic moment

μ_{n}

. If

μ_{n} α n^{x}

, the value of

x

is:

(A)2
(B)1✓ Correct
(C)3
(D)0

Answer: (B)

Solution

The magnetic moment of the orbiting electron is

μ = i A = (\frac{e v}{2 π r}) π r^{2} = \frac{e v r}{2}

From the Bohr model,

v \propto \frac{1}{n}

and

r \propto n^{2}

, so

μ \propto v \cdot r \propto \frac{1}{n} \times n^{2} = n

Hence

μ_{n} \propto n^{1}

, giving

x = 1

JEE Main · 2024 · 30 Jan 2024 · Shift 2 · Single correct option

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