Question

Gyromagnetic ratio of an electron is the ratio between

• A. charge and angular momentum
• B. magnetic moment and angular acceleration
• C. magnetic moment and angular momentum
• D. charge and angular momentum
• E. magnetic moment and angular velocity

Hint:

Gyromagnetic ratio always connects magnetic moment with angular momentum: \[ \gamma = \frac{\mu}{L} \]

Answer 1

The Correct Option is C

Step 1: Recall definition of gyromagnetic ratio.
Gyromagnetic ratio is defined as: \[ \gamma = \frac{\text{magnetic moment}}{\text{angular momentum}} \]

Step 2: Write the mathematical expression.
For an electron: \[ \gamma = \frac{\mu}{L} \] where \( \mu \) is magnetic moment and \( L \) is angular momentum.

Step 3: Understand physical meaning.
It represents how much magnetic moment is produced per unit angular momentum of a charged particle.

Step 4: Check units.
Magnetic moment has units: \[ A \cdot m^2 \] Angular momentum has units: \[ kg \cdot m^2 \cdot s^{-1} \] Their ratio gives gyromagnetic ratio.

Step 5: Eliminate incorrect options.
- Charge and angular momentum → incorrect definition
- Magnetic moment and angular acceleration → unrelated
- Magnetic moment and angular velocity → incorrect
Only magnetic moment and angular momentum match definition.

Step 6: Recall electron-specific relation.
For an electron: \[ \gamma = \frac{e}{2m} \] which comes from the ratio of magnetic moment to angular momentum.

Step 7: Final conclusion.
Hence, gyromagnetic ratio is: \[ \boxed{\frac{\text{magnetic moment}}{\text{angular momentum}}} \] Therefore, the correct option is \[ \boxed{(3)\ \text{magnetic moment and angular momentum}} \]