Question

An orbital having one radial node and two angular nodes may be:
a.) ${ 3d }_{ xy }$
b.) ${ 4d }_{ yz }$
c.) ${ 5d }_{ x^{ 2 }{ -y }^{ 2 } }$
d.) ${ 4p }_{ z }$

Answer 1

Hint:. Nodes are the spaces where the probability of finding an electron is zero.
Radial nodes are the nodes that appear along the radius of an atom while angular nodes are the nodes that appear along the plane of an angle.

Complete step by step answer:
The radial nodes are calculated as: n - l - 1
where, n - 1 = total amount of nodes present
l = angular nodes
It is given that, angular nodes = 2
It means, l = 2
For s, l = 0
For p, l = 1
For d, l = 2
For f, l = 3
So, l = 2 for d-orbital

As 1 radial node is present, use the formula
Radial node = n - l - 1
 1 = n - 2 - 1
 n = 1 + 3 = 4
So, the orbital will be ${ 4d }_{ yz }$
So, the correct answer is “Option A”.

Additional Information:
- The radial wave function depends on the principal and azimuthal quantum numbers, and the angular wave function depends on the azimuthal and magnetic quantum numbers.
- The radial function depicts the size of the orbital and the angular function determines the orientation of lobes of the orbital.
- Radial nodes have fixed radii whereas angular nodes have fixed angles.
- Radial nodes are spherical while angular nodes are planes or cones.

Note: The possibility to make a mistake is that you may confuse the term ‘n’. Here, n = the total number of nodes and not the principal quantum number.