The orbital having two radial as well as two angular nodes is

Options

A. 3p
B. 4f
C. 4d
D. 5d

Answer

To determine the orbital that has two radial nodes and two angular nodes, we can follow these steps:

### Step 1: Understand the formulas for nodes
- **Radial Nodes**: The number of radial nodes can be calculated using the formula:
\[ \text{Radial Nodes} = n - l - 1 \]
where \( n \) is the principal quantum number and \( l \) is the azimuthal quantum number.

- **Angular Nodes**: The number of angular nodes is equal to the value of \( l \).

### Step 2: Analyze the options
We will analyze each option given in the question to find out which orbital has the required nodes.

#### Option 1: 5d
- Here, \( n = 5 \) and for \( d \) orbital, \( l = 2 \).
- Calculate radial nodes:
\[ \text{Radial Nodes} = 5 - 2 - 1 = 2 \]
- Calculate angular nodes:
\[ \text{Angular Nodes} = l = 2 \]
- This option has 2 radial nodes and 2 angular nodes.

#### Option 2: 4f
- Here, \( n = 4 \) and for \( f \) orbital, \( l = 3 \).
- Calculate radial nodes:
\[ \text{Radial Nodes} = 4 - 3 - 1 = 0 \]
- This option has 0 radial nodes and 3 angular nodes.

#### Option 3: 3p
- Here, \( n = 3 \) and for \( p \) orbital, \( l = 1 \).
- Calculate radial nodes:
\[ \text{Radial Nodes} = 3 - 1 - 1 = 1 \]
- This option has 1 radial node and 1 angular node.

#### Option 4: 4d
- Here, \( n = 4 \) and for \( d \) orbital, \( l = 2 \).
- Calculate radial nodes:
\[ \text{Radial Nodes} = 4 - 2 - 1 = 1 \]
- This option has 1 radial node and 2 angular nodes.

### Step 3: Conclusion
From the analysis, only the 5d orbital has both 2 radial nodes and 2 angular nodes. Therefore, the correct answer is:

**5d orbital**