Which shell would be the first to have g sub-shell ?

Options

A. L
B. M
C. N
D. O

Answer

To determine which shell would be the first to have a g sub-shell, we need to analyze the principal quantum number (n) and the possible values of the azimuthal quantum number (l) for each shell.

### Step-by-Step Solution:

1. **Identify the Shells and Their Principal Quantum Numbers:**
- The shells are denoted as K, L, M, N, O, etc.
- Their corresponding principal quantum numbers (n) are:
- K shell: n = 1
- L shell: n = 2
- M shell: n = 3
- N shell: n = 4
- O shell: n = 5

2. **Understand the Values of l:**
- The azimuthal quantum number (l) can take values from 0 to (n-1).
- Each value of l corresponds to a specific sub-shell:
- l = 0 → s sub-shell
- l = 1 → p sub-shell
- l = 2 → d sub-shell
- l = 3 → f sub-shell
- l = 4 → g sub-shell

3. **Evaluate Each Shell:**
- **L Shell (n = 2):**
- Possible values of l: 0 to 1 (l = 0, 1)
- Sub-shells: s and p (no g sub-shell)
- **M Shell (n = 3):**
- Possible values of l: 0 to 2 (l = 0, 1, 2)
- Sub-shells: s, p, and d (no g sub-shell)
- **N Shell (n = 4):**
- Possible values of l: 0 to 3 (l = 0, 1, 2, 3)
- Sub-shells: s, p, d, and f (no g sub-shell)
- **O Shell (n = 5):**
- Possible values of l: 0 to 4 (l = 0, 1, 2, 3, 4)
- Sub-shells: s, p, d, f, and g (g sub-shell is present)

4. **Conclusion:**
- The first shell to have a g sub-shell is the O shell (n = 5).

### Final Answer:
The first shell to have a g sub-shell is the **O shell** (option D).

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