An electron has principal quantum number `3`. The number of its (i) sub-shell and (ii) orbitals would be respectively.

Options

A. `3 and 5`
B. `3 and 7`
C. `3 and 9`
D. `2 and 5`

Explanation

To solve the question, we need to determine the number of sub-shells and orbitals for an electron with a principal quantum number \( n = 3 \).

### Step-by-step Solution:

1. **Identify the Principal Quantum Number (n)**:
- The principal quantum number \( n \) is given as 3.

2. **Determine the Possible Values of the Azimuthal Quantum Number (l)**:
- The azimuthal quantum number \( l \) can take values from 0 to \( n-1 \).
- For \( n = 3 \), the possible values of \( l \) are:
- \( l = 0 \) (s sub-shell)
- \( l = 1 \) (p sub-shell)
- \( l = 2 \) (d sub-shell)

3. **Count the Number of Sub-shells**:
- Each value of \( l \) corresponds to a sub-shell:
- \( l = 0 \) corresponds to 1 sub-shell (s)
- \( l = 1 \) corresponds to 1 sub-shell (p)
- \( l = 2 \) corresponds to 1 sub-shell (d)
- Therefore, the total number of sub-shells is \( 3 \) (s, p, and d).

4. **Determine the Number of Orbitals in Each Sub-shell**:
- The number of orbitals in each sub-shell is defined as follows:
- For the s sub-shell (\( l = 0 \)): 1 orbital
- For the p sub-shell (\( l = 1 \)): 3 orbitals
- For the d sub-shell (\( l = 2 \)): 5 orbitals

5. **Calculate the Total Number of Orbitals**:
- Total orbitals = Number of orbitals in s + Number of orbitals in p + Number of orbitals in d
- Total orbitals = \( 1 + 3 + 5 = 9 \)

### Final Answer:
- The number of sub-shells is **3**.
- The number of orbitals is **9**.