The maximum number of electrons in a shell is given by expression

Options

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

Explanation

To find the maximum number of electrons that can occupy a shell, we use the formula:

**Maximum number of electrons (N) = 2n²**

Where:
- N is the maximum number of electrons in a shell.
- n is the principal quantum number (the shell number).

### Step-by-Step Solution:

1. **Identify the Shell Number (n)**:
- Each shell is designated by a principal quantum number (n). For example:
- K shell corresponds to n = 1
- L shell corresponds to n = 2
- M shell corresponds to n = 3
- N shell corresponds to n = 4, and so on.

2. **Apply the Formula**:
- To find the maximum number of electrons for a specific shell, substitute the value of n into the formula 2n².
- For example:
- For K shell (n = 1):
\[ N = 2(1)² = 2 \text{ electrons} \]
- For L shell (n = 2):
\[ N = 2(2)² = 8 \text{ electrons} \]
- For M shell (n = 3):
\[ N = 2(3)² = 18 \text{ electrons} \]
- For N shell (n = 4):
\[ N = 2(4)² = 32 \text{ electrons} \]

3. **Conclusion**:
- The general expression for the maximum number of electrons in any shell is:
\[ N = 2n² \]

### Final Answer:
The maximum number of electrons in a shell is given by the expression **2n²**.

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