A 4f orbital has

Options

A. one node
B. two nodes
C. three nodes
D. four nodes

Explanation

To determine the number of nodes in a 4f orbital, we can follow these steps:

### Step 1: Identify the Principal Quantum Number (n)
The principal quantum number (n) for the 4f orbital is 4.

### Step 2: Calculate Total Number of Nodes
The total number of nodes in an orbital can be calculated using the formula:
\[ \text{Total Nodes} = n - 1 \]
Substituting the value of n:
\[ \text{Total Nodes} = 4 - 1 = 3 \]

### Step 3: Identify the Azimuthal Quantum Number (l)
For f orbitals, the azimuthal quantum number (l) is 3.

### Step 4: Calculate Radial Nodes
Radial nodes can be calculated using the formula:
\[ \text{Radial Nodes} = n - l - 1 \]
Substituting the values:
\[ \text{Radial Nodes} = 4 - 3 - 1 = 0 \]

### Step 5: Calculate Angular Nodes
Angular nodes are equal to the value of l:
\[ \text{Angular Nodes} = l = 3 \]

### Step 6: Summarize Total Nodes
The total number of nodes is the sum of radial and angular nodes:
\[ \text{Total Nodes} = \text{Radial Nodes} + \text{Angular Nodes} = 0 + 3 = 3 \]

### Conclusion
Thus, the 4f orbital has a total of **3 nodes**.

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