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Question: If the angular momentum of an electron is \(\vec { J }\) then the magnitude of the magnetic moment w...

If the angular momentum of an electron is J⃗\vec { J } then the magnitude of the magnetic moment will be

A

eJm\frac { e J } { m }

B

eJ2m\frac { e J } { 2 m }

C

eJ 2m

D

2meJ\frac { 2 m } { e J }

Answer

eJ2m\frac { e J } { 2 m }

Explanation

Solution

As we know for circulating electron magnetic moment

M=12evrM = \frac { 1 } { 2 } e v r ...... (i)

and angular momentum J=mvrJ = m v r ...... (ii)

From equation (i) and (ii) M=eJ2mM = \frac { e J } { 2 m }