An electron revolving in Bohr orbit has magnetic moment If , the value of is

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Solution

Q.
An electron revolving in $n^{t h}$ Bohr orbit has magnetic moment $μ_{n} .$ If $μ_{n}$ $α$ $n^{x}$ , the value of $x$ is [2024]

1 2

2 1

3 3

4 0

Ans.
(2)

$Magnetic moment (m) = I A$

$= \frac{e}{T} \cdot π r^{2} = \frac{e}{(\frac{2 π r}{v})} \cdot π r^{2} = \frac{e r v}{2}$

$We know that r \propto n^{2} and v \propto \frac{1}{n}$

$S o μ \propto r v$

$μ \propto \frac{n^{2}}{n} \Rightarrow μ \propto n = 1$

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