What are the numbers of angular nodes and radial nodes for 4d orbitals respectively?

Options

A. 2 and 1
B. 1 and 2
C. 2 and 3
D. 3 and 2

Answer

To determine the number of angular nodes and radial nodes for the 4d orbitals, we can follow these steps:

### Step 1: Identify the Principal Quantum Number (n) and Azimuthal Quantum Number (l)
For the 4d orbital:
- The principal quantum number \( n = 4 \).
- The azimuthal quantum number \( l \) for d orbitals is \( l = 2 \).

### Step 2: Calculate the Number of Angular Nodes
The number of angular nodes is given by the formula:
\[ \text{Number of Angular Nodes} = l \]
Since \( l = 2 \) for d orbitals:
- Therefore, the number of angular nodes = 2.

### Step 3: Calculate the Number of Radial Nodes
The number of radial nodes is given by the formula:
\[ \text{Number of Radial Nodes} = n - l - 1 \]
Substituting the values we have:
- \( n = 4 \)
- \( l = 2 \)

Calculating:
\[ \text{Number of Radial Nodes} = 4 - 2 - 1 = 1 \]

### Final Answer
- The number of angular nodes for the 4d orbital is **2**.
- The number of radial nodes for the 4d orbital is **1**.

### Summary
- Angular Nodes: 2
- Radial Nodes: 1

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