Question

The mathematical basis for Nuclear Magnetic Resonance (NMR) states that if $\mu$ is the nuclear magnetic moment of the molecule, the gyromagnetic ratio is proportional to:

• A. $\mu$
• B. $\dfrac{1}{\mu}$
• C. $\sqrt{\mu}$
• D. $\mu^2$

Hint:

In NMR theory, the gyromagnetic ratio depends directly on the nuclear magnetic moment $\mu$ — more $\mu$, stronger resonance.

Answer 1

The Correct Option is A

In Nuclear Magnetic Resonance (NMR), the gyromagnetic ratio ($\gamma$) is a fundamental property of a nucleus that determines how it behaves in a magnetic field.
The gyromagnetic ratio is defined as the ratio of the magnetic moment ($\mu$) to the angular momentum ($J$) of the nucleus:
\[ \gamma = \dfrac{\mu}{J} \]
Since $J$ is typically fixed for a given nucleus, the gyromagnetic ratio $\gamma$ becomes directly proportional to the magnetic moment $\mu$.
This proportionality is essential in determining the resonance frequency of a nucleus in a magnetic field, which is given by:
\[ f = \dfrac{\gamma B}{2\pi} \]
Thus, the correct relationship is: $\gamma \propto \mu$.