Of the following states, `5s,3p,4f,5p,4g,3d, and 2p`, the one which is NOT allowed is

Options

A. 3p
B. 4f
C. 3d
D. 4g

Answer

To determine which of the given states is NOT allowed, we need to apply the rules governing quantum numbers in atomic physics. The principal quantum number (n) and the azimuthal quantum number (l) must adhere to specific relationships.

### Step-by-Step Solution:

1. **Understand Quantum Numbers**:
- The principal quantum number (n) indicates the energy level of an electron in an atom and can take positive integer values (1, 2, 3, ...).
- The azimuthal quantum number (l) indicates the subshell and can take integer values from 0 to (n-1). The values of l correspond to different subshells:
- s (l=0), p (l=1), d (l=2), f (l=3), g (l=4), etc.

2. **Analyze Each State**:
- **5s**: Here, n = 5 and l = 0 (s). Since l < n, this state is allowed.
- **3p**: Here, n = 3 and l = 1 (p). Since l < n, this state is allowed.
- **4f**: Here, n = 4 and l = 3 (f). Since l < n, this state is allowed.
- **5p**: Here, n = 5 and l = 1 (p). Since l < n, this state is allowed.
- **4g**: Here, n = 4 and l = 4 (g). Since l is equal to n, this state is NOT allowed.
- **3d**: Here, n = 3 and l = 2 (d). Since l < n, this state is allowed.
- **2p**: Here, n = 2 and l = 1 (p). Since l < n, this state is allowed.

3. **Conclusion**: The only state that is NOT allowed is **4g**.

### Final Answer:
The state which is NOT allowed is **4g**.

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