What is the maximum number of electrons which can be accommodated in an atom in which the highest principal quantum number is 4 ?

Options

A. 10
B. 18
C. 36
D. 54

Explanation

To determine the maximum number of electrons that can be accommodated in an atom where the highest principal quantum number (n) is 4, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Principal Quantum Number (n):**
The principal quantum number (n) indicates the energy level of an electron in an atom. For n = 4, we consider the energy levels from n = 1 to n = 4.

2. **Identify the Electron Configuration:**
The electron configuration fills the orbitals in the following order based on increasing energy levels:
- 1s
- 2s
- 2p
- 3s
- 3p
- 4s
- 3d
- 4p
- 4d
- 4f
- 5s, etc.

3. **Count the Maximum Electrons in Each Subshell:**
The maximum number of electrons that can occupy each subshell is given by the formula \(2n^2\):
- For n = 1: 1s → 2 electrons
- For n = 2: 2s → 2 electrons, 2p → 6 electrons (Total for n=2: 2 + 6 = 8 electrons)
- For n = 3: 3s → 2 electrons, 3p → 6 electrons, 3d → 10 electrons (Total for n=3: 2 + 6 + 10 = 18 electrons)
- For n = 4: 4s → 2 electrons, 4p → 6 electrons (Total for n=4: 2 + 6 = 8 electrons)

4. **Summing Up the Electrons:**
Now, we add the maximum number of electrons from all the energy levels up to n = 4:
- From n = 1: 2 electrons
- From n = 2: 8 electrons
- From n = 3: 18 electrons
- From n = 4: 8 electrons

Total = \(2 + 8 + 18 + 8 = 36\) electrons.

5. **Conclusion:**
Therefore, the maximum number of electrons that can be accommodated in an atom with the highest principal quantum number of 4 is **36 electrons**.