The radial probability distribution curve obtained for an orbital wave function has 3 peaks and 2 radial nodes. The valence electron of which one of the following metals does this wave function correspond to ? 

Options

A. Cu
B. Li
C. K
D. Na

Answer

To determine the valence electron configuration corresponding to the given radial probability distribution curve with 3 peaks and 2 radial nodes, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Information**:
- The radial probability distribution curve has 3 peaks, indicating the principal quantum number (n) is 3.
- There are 2 radial nodes.

2. **Relate Nodes to Quantum Numbers**:
- The number of radial nodes can be calculated using the formula:
\[ \text{Number of radial nodes} = n - l - 1 \]
- Given that there are 2 radial nodes, we can set up the equation:
\[ 2 = n - l - 1 \]
- Substituting \( n = 3 \):
\[ 2 = 3 - l - 1 \implies l = 0 \]

3. **Identify the Orbital**:
- With \( n = 3 \) and \( l = 0 \), the corresponding orbital is the 3s orbital.

4. **Determine the Valence Electron Configuration**:
- Now, we need to find which of the given metals has its valence electron in the 3s orbital. The metals provided are:
- Copper (Cu, atomic number 29)
- Lithium (Li, atomic number 3)
- Potassium (K, atomic number 19)
- Sodium (Na, atomic number 11)

5. **Write the Electron Configurations**:
- **Copper (Cu)**:
- Atomic number 29: \( 1s^2 2s^2 2p^6 3s^2 3p^6 3d^{10} 4s^1 \) (Valence electron in 4s)
- **Lithium (Li)**:
- Atomic number 3: \( 1s^2 2s^1 \) (Valence electron in 2s)
- **Potassium (K)**:
- Atomic number 19: \( 1s^2 2s^2 2p^6 3s^2 3p^6 4s^1 \) (Valence electron in 4s)
- **Sodium (Na)**:
- Atomic number 11: \( 1s^2 2s^2 2p^6 3s^1 \) (Valence electron in 3s)

6. **Identify the Correct Metal**:
- From the configurations, only Sodium (Na) has its valence electron in the 3s orbital.

### Conclusion:
The valence electron of the metal that corresponds to the given wave function is Sodium (Na).