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 of choosing the correct statement regarding the structure of an atom, we will analyze each statement provided.

### Step-by-Step Solution:

1. **Understanding the Number of Orbitals in the n-th Shell**:
- The number of orbitals in the n-th shell is given by the formula \( n^2 \).
- For example, if \( n = 4 \), the number of orbitals would be \( 4^2 = 16 \).
- **Conclusion**: The first statement claiming the number of orbitals in the n-th shell is \( n \) is incorrect.

2. **Analyzing the Second Statement**:
- The second statement claims that the number of orbitals in the n-th shell is equal to 3.
- As established, the number of orbitals in the n-th shell is \( n^2 \), which can never be just 3 for any \( n \) greater than or equal to 2.
- **Conclusion**: The second statement is also incorrect.

3. **Understanding the Number of Orbitals in a Sub-shell**:
- The number of orbitals in a sub-shell is given by the formula \( 2L + 1 \), where \( L \) is the azimuthal quantum number.
- For example, for a P orbital where \( L = 1 \), the number of orbitals is \( 2(1) + 1 = 3 \).
- For a D orbital where \( L = 2 \), the number of orbitals is \( 2(2) + 1 = 5 \).
- **Conclusion**: The statement regarding the number of orbitals in a sub-shell being \( 2L - 1 \) is incorrect.

4. **Determining the Number of Sub-shells in the n-th Shell**:
- The number of sub-shells in the n-th shell is given by \( n \).
- The value of \( L \) for the sub-shells ranges from 0 to \( n-1 \), which means there are \( n \) possible sub-shells.
- **Conclusion**: The statement about the number of sub-shells being \( n-1 \) is incorrect.

5. **Analyzing the Number of Electrons in an Orbital**:
- The maximum number of electrons in an orbital is 2.
- The statement about the number of electrons in a sub-shell being \( 4L + 2 \) is also incorrect, as it should be \( 2(2L + 1) \) for the total number of electrons in a sub-shell.
- **Conclusion**: The statement regarding the number of electrons in an orbital is incorrect.

### Final Conclusion:
None of the statements provided are correct based on the analysis above.