Question

The nuclear spin quantum number (\( l \)) of a nucleus is \( \frac{3}{2} \). When placed in an external magnetic field, the number of possible spin energy states it can occupy is ...........

Hint:

The number of spin energy states for a nucleus is calculated by \( 2l + 1 \), where \( l \) is the spin quantum number.

Answer 1

Correct Answer: 4

Step 1: Understanding the spin quantum number.
The spin quantum number \( l \) gives the possible orientations of the spin in an external magnetic field. The number of energy states that a nucleus can occupy is given by \( 2l + 1 \), where \( l \) is the spin quantum number.

Step 2: Calculation of the number of spin energy states.
For \( l = \frac{3}{2} \), the number of possible energy states is: \[ 2l + 1 = 2 \times \frac{3}{2} + 1 = 4 \]

Step 3: Conclusion.
The number of possible spin energy states the nucleus can occupy is 4.