Question 309: Dual Nature of Matter and Radiation

Question

The gyromagnetic ratio and Bohr magneton are given respectively by [Given $\rightarrow \mathrm{e}=$ charge on electron, $\mathrm{m}=$ mass of electron, $\mathrm{h}=$ Planck's constant]

Accepted Answer

The gyromagnetic ratio is given by the expression:
$$ \frac{e}{2m} $$
This ratio describes the magnetic moment of a system per unit angular momentum. It is especially prominent in the context of electron spin and nuclear magnetic resonance.
The Bohr magneton, which represents the natural unit of the magnetic moment in atomic physics, is given by:
$$ \frac{e\hbar}{2m} $$
where $\hbar$ is the reduced Planck's constant, defined as $\hbar = \frac{h}{2\pi}$.
For the given options, the correct expressions describing the gyromagnetic ratio and the Bohr magneton are found in Option A:
Gyromagnetic Ratio: $$ \frac{e}{2m} $$
Bohr Magneton: $$ \frac{eh}{4\pi m} $$ (since $\hbar = \frac{h}{2\pi}$, this simplifies to the Bohr magneton from the definition with $\hbar$)
Thus, Option A is the correct choice which matches these definitions.

Answer

$\frac{\mathrm{e}}{2 \mathrm{~m}}, \frac{\mathrm{eh}}{4 \pi \mathrm{~m}}$

Answer

$\frac{\mathrm{eh}}{4 \pi \mathrm{~m}}, \frac{\mathrm{e}}{2 \mathrm{~m}}$

Answer

$\frac{2 \mathrm{~m}}{\mathrm{e}}, \frac{4 \pi \mathrm{~m}}{\mathrm{eh}}$

Answer

$\frac{4 \pi \mathrm{~m}}{\mathrm{eh}}, \frac{2 \mathrm{~m}}{\mathrm{e}}$

Dual Nature of Matter and Radiation

The gyromagnetic ratio and Bohr magneton are given respectively by [Given \rightarrow \mathrm{e}= charge on electron, \mathrm{m}= mass of electron, \mathrm{h}= Planck's constant]

Choose the correct answer: