Question

How many radial nodes are there in 5f orbitals?
(A) 1
(B) 0
(C) 2
(D) 3

Answer 1

Hint: Recollect what a node is. Find out the meaning of a radial node. The formula for calculating the number of radial nodes is n – l – 1 where n is the principal quantum number and l is the azimuthal quantum number. Just substitute the values and find out the answer.

Complete step by step answer:
- A node is a space in the atom where the probability of finding an electron is zero.
- A node will always have zero electron density at any given point of time.
- There are two types of nodes viz, radial node and angular node.
- A radial node is a spheric node whereas an angular node is a planar node.
- The number of radial nodes is calculated using the formula, n – l – 1 where n is the principal quantum number and l is the azimuthal quantum number.
- The principal quantum number represents the main-shell in which an electron enters and is denoted as ‘n’. The value of ‘n’ is a natural integer 1, 2, 3, 4, 5, 6, 7.
- The azimuthal quantum number represents the sub-shell in which an electron is present and it is denoted by ‘l’. The value of ‘l’ is a whole integer where s = 0, p = 1, d = 2 and f = 3.
- For 5f orbitals, n = 5 and l = 3.
- Therefore, number of radial nodes will be, n – l – 1 = 5 – 3 – 1 = 5 – 4 = 1
- Therefore, the number of radial nodes in 5f orbitals is 1.
Therefore, the answer is option (A).

Note: Remember the number of radial nodes in any orbital is calculated using the formula, n-l-1. A node is an area in space where the probability of finding an electron is zero. A node has zero electron density. An antinode is the place where the probability of finding an electron is maximum.