Maximum number of electrons that can be accommodated in shell with n = `4` are:

Options

A. `72`
B. `16`
C. `32`
D. `50`

Answer

To determine the maximum number of electrons that can be accommodated in a shell with a principal quantum number \( n = 4 \), we can use the formula:

\[ \text{Maximum number of electrons} = 2n^2 \]

### Step-by-step solution:

1. **Identify the principal quantum number (n)**:
- Here, \( n = 4 \).

2. **Substitute the value of n into the formula**:
- We will substitute \( n \) into the formula \( 2n^2 \).
- So, we have:
\[ 2n^2 = 2(4^2) \]

3. **Calculate \( n^2 \)**:
- First, calculate \( 4^2 \):
\[ 4^2 = 16 \]

4. **Multiply by 2**:
- Now, substitute back into the equation:
\[ 2(16) = 32 \]

5. **Conclusion**:
- Therefore, the maximum number of electrons that can be accommodated in the shell with \( n = 4 \) is \( 32 \).

### Final Answer:
The maximum number of electrons that can be accommodated in a shell with \( n = 4 \) is **32**.