The total number of electrons present in any main energy level can be calculated from

Options

A. `(2l+1)`
B. `2n^(2)`
C. `(2n+1)`
D. `n^(2)`

Explanation

To determine the total number of electrons present in any main energy level, we can use the formula:

**Total number of electrons = 2n²**

Where:
- **n** = principal quantum number (which indicates the main energy level).

### Step-by-Step Solution:

1. **Identify the Principal Quantum Number (n)**:
- The principal quantum number (n) indicates the main energy level of an atom. It can take positive integer values (1, 2, 3, ...).

2. **Use the Formula**:
- To find the total number of electrons in a given main energy level, substitute the value of n into the formula:
\[ \text{Total electrons} = 2n^2 \]

3. **Calculate for Different Values of n**:
- For **n = 1** (K shell):
\[ \text{Total electrons} = 2(1^2) = 2 \text{ electrons} \]
- For **n = 2** (L shell):
\[ \text{Total electrons} = 2(2^2) = 2 \times 4 = 8 \text{ electrons} \]
- For **n = 3** (M shell):
\[ \text{Total electrons} = 2(3^2) = 2 \times 9 = 18 \text{ electrons} \]
- For **n = 4** (N shell):
\[ \text{Total electrons} = 2(4^2) = 2 \times 16 = 32 \text{ electrons} \]

4. **Conclusion**:
- The total number of electrons in any main energy level can be calculated using the formula \(2n^2\), where n is the principal quantum number. This allows us to find the maximum number of electrons that can occupy each energy level.