Choose the correct statement among the following:

Options

A. Number of orbitals in `n^(th)` shell is n.
B. Number of orbitals in a subshell is `(2l-1)`.
C. Number of subshells in `n^(th)` shell is (n-1).
D. Number of electrons in an orbital of a subshell is `2(2l+1)`.

Answer

To solve the question, we need to analyze the statements provided and determine which one is correct based on our understanding of atomic structure.

### Step-by-Step Solution:

1. **Understanding the First Statement**:
- The statement claims that the number of orbitals in the nth shell is n.
- This is incorrect. The number of orbitals in the nth shell is actually given by \( n^2 \). For example, in the second shell (n=2), there are 4 orbitals (1s and 3p).

2. **Evaluating the Second Statement**:
- The second statement claims that the number of orbitals in a sub-shell is \( 2l - 1 \).
- This is also incorrect. The correct formula for the number of orbitals in a sub-shell is \( 2l + 1 \). For example, for the p sub-shell (where \( l = 1 \)), there are 3 orbitals (not 1).

3. **Analyzing the Third Statement**:
- The third statement claims that the number of sub-shells in the nth shell is \( n - 1 \).
- This is incorrect. The number of sub-shells in the nth shell is actually equal to n. For example, in the second shell (n=2), there are 2 sub-shells (s and p).

4. **Checking the Fourth Statement**:
- The fourth statement claims that the number of electrons in an orbital of a sub-shell is \( 2(2l + 1) \).
- This statement is misleading. The correct interpretation is that the maximum number of electrons in a sub-shell is \( 2(2l + 1) \). For example, for the p sub-shell (l=1), the maximum number of electrons is 6 (which is \( 2 \times 3 \)). Thus, this statement is correct.

### Conclusion:
The correct statement among the options provided is the fourth statement: "The number of electrons in an orbital of a sub-shell is \( 2(2l + 1) \)."