Question:
The number of radial nodes and angular nodes of a \(4f\)-orbital are respectively
The number of radial nodes and angular nodes of a \(4f\)-orbital are respectively
Show Hint
For any orbital:
\[
\text{Total nodes}=n-1
\]
\[
\text{Radial nodes}=n-l-1
\]
\[
\text{Angular nodes}=l
\]
Updated On: Jun 15, 2026
- \(0,\,3\)
- \(1,\,2\)
- \(2,\,1\)
- \(2,\,0\)
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The Correct Option is A
Solution and Explanation
Step 1: Recall the formulas for nodes.
For an orbital,
\[ \text{Radial nodes}=n-l-1 \] and
\[ \text{Angular nodes}=l \] where,
\[ n=\text{principal quantum number} \] \[ l=\text{azimuthal quantum number} \]
Step 2: Identify the quantum numbers for \(4f\)-orbital.
For a \(4f\)-orbital,
\[ n=4 \] For \(f\)-orbital,
\[ l=3 \]
Step 3: Calculate the number of radial nodes.
\[ \text{Radial nodes}=4-3-1 \] \[ =0 \]
Step 4: Calculate the number of angular nodes.
\[ \text{Angular nodes}=l=3 \]
Step 5: Final conclusion.
Hence, the number of radial nodes and angular nodes respectively are
\[ \boxed{0,\,3} \]
For an orbital,
\[ \text{Radial nodes}=n-l-1 \] and
\[ \text{Angular nodes}=l \] where,
\[ n=\text{principal quantum number} \] \[ l=\text{azimuthal quantum number} \]
Step 2: Identify the quantum numbers for \(4f\)-orbital.
For a \(4f\)-orbital,
\[ n=4 \] For \(f\)-orbital,
\[ l=3 \]
Step 3: Calculate the number of radial nodes.
\[ \text{Radial nodes}=4-3-1 \] \[ =0 \]
Step 4: Calculate the number of angular nodes.
\[ \text{Angular nodes}=l=3 \]
Step 5: Final conclusion.
Hence, the number of radial nodes and angular nodes respectively are
\[ \boxed{0,\,3} \]
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