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Physics · 2025 · 3 marks
CBSE 2025 · Region 5 · Set 1 · Q26
An electron of mass m and charge - e is revolving anticlockwise around the nucleus of an atom. (a) Obtain the expression for the magnetic dipole…
An electron of mass m and charge - e is revolving anticlockwise around the nucleus of an atom.
(a)
Obtain the expression for the magnetic dipole moment ( $\displaystyle \mu$ ) of the atom.
(b)
If $\displaystyle \overrightarrow{\mathrm{L}}$ is the angular momentum of electron, show that \[\vec{\mu}=-\left(\frac{\mathrm{e}}{2 \mathrm{~m}}\right) \overrightarrow{\mathrm{L}} . \]
Marking-scheme solution
(a)
$\displaystyle \mu=I A$
$\displaystyle =\frac{e}{T} \times A$
$\displaystyle =\frac{e}{\dfrac{2 \pi r}{v}} \times \pi r^{2}$
$\displaystyle =\frac{1}{2} e v r$
(b)
$\displaystyle L=m v r$
$\displaystyle \mu=\frac{e v r \times m}{2 \times m}$
$\displaystyle =\left(\frac{e}{2 m}\right) L$
Direction of $\displaystyle \vec{\mu}$ is opposite to that of $\displaystyle \vec{L}$:
$\displaystyle \vec{\mu}=-\left(\frac{e}{2 m}\right) \vec{L}$
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CBSE Class 12 Physics past-paper question from the 2025 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.