Maximum number of electrons in any orbit is

Options

A. `n^2`
B. `2n^2`
C. `1//2 n^2`
D. None of these

Explanation

To determine the maximum number of electrons that can occupy any orbit (or shell) in an atom, we can use the formula:

### Step-by-Step Solution:

1. **Understand the Concept of Electron Shells**:
- Atoms have a nucleus surrounded by shells where electrons are arranged. Each shell can hold a certain maximum number of electrons.

2. **Identify the Formula**:
- The maximum number of electrons in any shell is given by the formula:
\[ \text{Maximum electrons} = 2n^2 \]
- Here, \( n \) represents the principal quantum number, which corresponds to the shell number.

3. **Determine the Shells**:
- The shells are designated as K, L, M, N, etc.
- For each shell:
- K shell (n=1)
- L shell (n=2)
- M shell (n=3)
- N shell (n=4), and so on.

4. **Calculate Maximum Electrons for Each Shell**:
- For K shell (n=1):
\[ \text{Maximum electrons} = 2(1^2) = 2 \]
- For L shell (n=2):
\[ \text{Maximum electrons} = 2(2^2) = 8 \]
- For M shell (n=3):
\[ \text{Maximum electrons} = 2(3^2) = 18 \]
- For N shell (n=4):
\[ \text{Maximum electrons} = 2(4^2) = 32 \]

5. **Conclusion**:
- The maximum number of electrons that can occupy any orbit (or shell) depends on the value of \( n \) and can be calculated using the formula \( 2n^2 \). Therefore, the maximum number of electrons in any orbit can be calculated based on the shell number.

### Final Answer:
The maximum number of electrons in any orbit is calculated using the formula \( 2n^2 \), where \( n \) is the shell number.

---