Question

The number of angular and radial nodes of 4d orbital respectively are:
A.3, 1
B.1, 2
C.3, 0
D.2, 1

Answer 1

Hint: A node in atomic structure is defined as a place in an atom where the probability of finding an electron is zero. In an atom, there are two nodes: one is the radial nodes and the other one is angular nodes.

Formula used: ${\text{r}} = {\text{n}} - {\text{l}} - 1$
where, n is the principal quantum number and l is the azimuthal quantum number.
Total no. of nodes = ${\text{n}} - 1$

Complete step by step answer:
A radial node is a sphere that occurs when the radial wave function of the atomic orbital is zero or the sign of the wave-function changes. On the other hand, angular nodes are either x, y, or z planes where the electrons aren’t present.
The number of radial nodes can be solved on the basis of the following equation:
${\text{r}} = {\text{n}} - {\text{l}} - 1$
The formula for total number of nodes is, ${\text{n}} - 1$
Therefore angular nodes = total nodes-radial nodes.
For the 4d orbital, n = 4 and l = 2
Therefore, r = $4 - 2 - 1$ ; r = 1.
Total number of nodes = $4 - 1 = 3$
Therefore the \[{\text{angular nodes }} = {\text{total nodes}} - {\text{radial nodes}}\] = $3 - 1 = 2$
Therefore the 4d orbital has 1 radial node and 2 angular nodes.

Hence, the correct answer is option B.

Note:
1.There are no nodes in the s-subshell of any orbit and also in the first orbit of an atom.
2.As the distance of the orbitals from the nucleus increases, the number of nodes also increases.
3.Radial nodes are specifically those that are present inside the orbital lobes while angular ones are those that present on the axial planes.