The maximum number of electrons in an atom which can have n=4 is

Options

A. 4
B. 8
C. 16
D. 32

Answer

To determine the maximum number of electrons in an atom with a principal quantum number \( n = 4 \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Principal Quantum Number (n)**:
- The principal quantum number \( n \) indicates the energy level of an electron in an atom. In this case, \( n = 4 \).

2. **Determine the Azimuthal Quantum Number (l)**:
- The azimuthal quantum number \( l \) can take values from \( 0 \) to \( n-1 \). Therefore, for \( n = 4 \), the possible values of \( l \) are:
- \( l = 0 \) (s subshell)
- \( l = 1 \) (p subshell)
- \( l = 2 \) (d subshell)
- \( l = 3 \) (f subshell)

3. **Identify the Maximum Electrons in Each Subshell**:
- Each subshell can hold a specific maximum number of electrons:
- The s subshell can hold a maximum of 2 electrons.
- The p subshell can hold a maximum of 6 electrons.
- The d subshell can hold a maximum of 10 electrons.
- The f subshell can hold a maximum of 14 electrons.

4. **Calculate the Total Maximum Electrons**:
- Now, we add the maximum number of electrons from each subshell:
\[ \text{Total electrons} = 2 \, (\text{s}) + 6 \, (\text{p}) + 10 \, (\text{d}) + 14 \, (\text{f}) = 32 \, \text{electrons} \]

5. **Conclusion**:
- The maximum number of electrons in an atom with \( n = 4 \) is **32**.