In an atom, an electron with charge 'e' and mass \( m \) is revolving around the nucleus in a specific orbit with angular momentum \( (\vec{L}) \) and the equivalent magnetic dipole moment \( (\mu) \) of that atom is: \( \vec{\mu} = -\displaystyle\frac{e}{2m}\vec{L} \), where \( \displaystyle\frac{e}{2m} \) will be:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Gyromagnetic ratio
A revolving electron is a current loop. For an orbit of radius \( r \) and speed \( v \), the current is \( I = ev/(2\pi r) \), so the magnetic moment and the angular momentum are
\( \displaystyle \mu = I\,\pi r^{2} = \frac{e v r}{2}, \qquad L = m v r \)
\( \displaystyle \frac{\mu}{L} = \frac{e}{2m} \)
The ratio of the magnetic moment to the angular momentum is called the gyromagnetic ratio; the minus sign only shows that \( \vec{\mu} \) is opposite to \( \vec{L} \) because the electron is negative.
Option (1) Bohr's magneton — Incorrect. The Bohr magneton \( eh/(4\pi m) \) is a magnetic moment (that of the first Bohr orbit), not a ratio of moment to angular momentum.
Option (2) Gyromagnetic ratio — Correct. \( e/2m = \mu/L \) is the gyromagnetic ratio.
Option (3) Specific charge of electron — Incorrect. The specific charge of the electron is \( e/m \), twice this ratio.
Option (4) Orbital magnetic moment — Incorrect. The orbital magnetic moment is \( \vec{\mu} \) itself, not the factor \( e/2m \) that multiplies \( \vec{L} \).
Note: This question is from the pre-rationalised NCERT book (2022-23). The topic was removed from the latest NCERT book (2026-27), and it also appears to be out of the CUET 2026 syllabus.
NCERT (Pre-rationalised edition, 2022-23):
The Magnetic Dipole Moment of a Revolving Electron – “… The ratio
\( \displaystyle \frac{\mu_l}{l} = \frac{e}{2m_e} \qquad (4.35) \)
is called the gyromagnetic ratio and is a constant.”