The number of radial nodes in 4s and 3p orbitals are respectively

Options

A. 2,0
B. 3,1
C. 2,2
D. 3,2

Answer

To find the number of radial nodes in the 4s and 3p orbitals, we can use the formula:

**Number of Radial Nodes = n - l - 1**

Where:
- **n** is the principal quantum number.
- **l** is the azimuthal quantum number.

### Step-by-Step Solution:

1. **Identify the quantum numbers for 4s orbital:**
- For the 4s orbital:
- Principal quantum number (n) = 4
- Azimuthal quantum number (l) = 0 (since s orbitals have l = 0)

2. **Calculate the number of radial nodes for 4s:**
- Using the formula:
\[ \text{Number of Radial Nodes} = n - l - 1 \]
- Substitute the values:
\[ \text{Number of Radial Nodes} = 4 - 0 - 1 = 3 \]
- Therefore, the number of radial nodes in the 4s orbital is **3**.

3. **Identify the quantum numbers for 3p orbital:**
- For the 3p orbital:
- Principal quantum number (n) = 3
- Azimuthal quantum number (l) = 1 (since p orbitals have l = 1)

4. **Calculate the number of radial nodes for 3p:**
- Using the same formula:
\[ \text{Number of Radial Nodes} = n - l - 1 \]
- Substitute the values:
\[ \text{Number of Radial Nodes} = 3 - 1 - 1 = 1 \]
- Therefore, the number of radial nodes in the 3p orbital is **1**.

5. **Final Answer:**
- The number of radial nodes in the 4s and 3p orbitals are **3 and 1**, respectively.