Question

Which of the following orbitals will have a radial node?

• A. 1s orbital
• B. 2s orbital
• C. 2p orbital
• D. 3d orbital

Hint:

The formula for calculating the number of nodes is n - l - 1 where n represents the principal quantum number and l represents the azimuthal quantum number. The ‘s’ orbital has an azimuthal quantum number of 0, and the radial nodes are spherical in shape, while angular nodes are planar and occur only in non-s orbitals.

Answer 1

The Correct Option is B

A radial node is a region in an atomic orbital where the radial probability density function (the probability of finding an electron at a certain distance from the nucleus) is zero. The number of radial nodes for an atomic orbital can be calculated using the formula:
[ Radial Nodes = n - l - 1 ]
where:
• (n) is the principal quantum number
• (l) is the azimuthal quantum number
Let’s analyze each given orbital:
• 1s orbital: (n = 1), (l = 0). Radial nodes = 1 - 0 - 1 = 0.
• 2s orbital: (n = 2), (l = 0). Radial nodes = 2 - 0 - 1 = 1.
• 2p orbital: (n = 2), (l = 1). Radial nodes = 2 - 1 - 1 = 0.
• 3d orbital: (n = 3), (l = 2). Radial nodes = 3 - 2 - 1 = 0.
Only the 2s orbital has a radial node based on this calculation, while the 1s, 2p, and 3d orbitals do not have radial nodes.