Question

The number of angular and radial nodes of 4d orbitals respectively are -
(A) 3, 1
(B) 1, 2
(C) 3, 0
(D) 2, 1

Answer 1

Hint: We have two main theories of atomic structure. Bohr’s model of atom, which considers electrons as a particle and Quantum Mechanical Model of atom which considers electrons to have wave nature associated with it. For this question, we should consider Quantum Mechanical Model of Atom.

Formula used: Angular node = l
Radial node = (n - l - 1)
Where,
l is the Azimuthal quantum number.
n is principal Quantum number.

Complete step by step answer:
Node is a place where the probability of finding an electron is zero.
An angular node is the number of planar regions where the electron density is zero. Or we can also say that it is a region where the angular wave function is zero. It is also known as nodal plane. It is a plane which passes through the nucleus. Angular nodes are given by the azimuthal quantum number (l).
Radial node is the spherical region where the electron density is zero.
Radial node is equal to n - l - 1.
Where,
n is the principal quantum number
l is azimuthal quantum number
The value of the principal quantum number refers to the shell in which the electron is placed. Therefore, for 4d orbital, n = 4
We know that, azimuthal quantum number (l) for d orbital is l = 2
Thus, be using above explanation, we can say
Angular node for 4d orbital is l = 2
Radial node for 4d orbital is (n - l - 1) = (4 - 2 - 1) = 1 $\left( {\because n = 4,l = 2} \right)$

Therefore, from the above explanation, the correct answer is, option (D) 2,1.

Note: Angular node is not necessarily a planar node. It could be a non-planar node. It is a flat plane. A radial node is a sphere. When the Radial part of the wave function is zero then it is a radial node.