The number of radial nodes and angular nodes of a $4f$-orbital are respectively

Question

Given below are two statements:
Statement (I): For a given shell, the total number of allowed orbitals is given by $ n^2 $.
Statement (II): For any subshell, the spatial orientation of the orbitals is given by $ -l $ to $ +l $ values including zero. In the light of the above statements, choose the correct answer from the options given below:

Answer 1

Step 1: Know the two kinds of nodes.
Every orbital can have radial nodes (spherical surfaces where the wavefunction is zero) and angular nodes (planar or conical surfaces). The two are counted by separate rules.
Step 2: Write the formulas.
Number of angular nodes equals the azimuthal quantum number $l$, and number of radial nodes equals $n - l - 1$, where $n$ is the principal quantum number.
Step 3: Read off n for the 4f orbital.
The digit in front of the orbital symbol is $n$, so for a $4f$ orbital, $n = 4$.
Step 4: Read off l for an f orbital.
The letters $s, p, d, f$ correspond to $l = 0, 1, 2, 3$. Thus for an $f$ orbital, $l = 3$.
Step 5: Compute both node counts.
Angular nodes $= l = 3$. Radial nodes $= n - l - 1 = 4 - 3 - 1 = 0$.
Step 6: State the answer in the asked order.
The question asks radial nodes first, then angular nodes, giving $0$ and $3$, which is option (1). \[ \boxed{0,\,3} \]

The number of radial nodes and angular nodes of a \(4f\)-orbital are respectively

Show Hint

The Correct Option is A

Solution and Explanation

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