Question

How many nodes are in $4f$ orbital.

Answer 1

Hint: Nodes are the region around the nucleus of an atom where probability of finding the electron is minimum. Here the probability of finding electrons is zero. Whereas at an antinode the probability of finding an electron is maximum.

Complete answer:
The maximum number of orbitals for any atom in the case of $4f$ is seven. In these orbitals there are nodes and antinodes. Nodes are regions where the electron finding probability is minimum or we can say it is zero. Thus it is hard to find any electron in any node. While at the antinode region the probability of finding the electron is maximum. Nodes are of two types:
$1.$ Radial Nodes
$2.$ Angular Nodes
 The number of nodes has a relation with the quantum number. The number of angular nodes for an orbital is equal to its azimuthal quantum number $\left( l \right)$ . For $4f$ , $l$ is equal to $3$ . Thus it has three angular nodes. The number of radial nodes is given by the formula:
Radial nodes ${\text{ = n - l - 1}}$
Therefore the sum of radial nodes and the angular nodes will give us the total number of nodes present in the $4f$ orbital. Thus a total of three nodes are present in the $4f$ orbital.

Note:
A radial node is generally a spherical surface around the nucleus of the atom. The angular node is generally a flat plane surface. However it may be in conical form also. These orbitals are found in f block elements which start from atomic number $57$ to atomic number $71$. In total there are $15$ elements. It is a complex orbital to study.