To solve this problem, we need to understand the concept of radial and angular nodes in atomic orbitals. The formulae to determine the number of radial and angular nodes are:
The number of radial nodes is given by \( n - l - 1 \).
The number of angular nodes is equal to the azimuthal quantum number \( l \).
Given that we are dealing with a 4d orbital:
The principal quantum number \( n \) is 4.
The azimuthal quantum number \( l \) for a d orbital is 2.
Now, let's calculate the nodes:
Radial nodes:
n - l - 1 = 4 - 2 - 1 = 1
Angular nodes:
l = 2
Therefore, the 4d orbital has 1 radial node and 2 angular nodes.
