Question

The number of radial nodes, nodal planes for an orbital with n=4; l=1 is:
A. $3$,$1$
B. $2$,$1$
C. $2$,$0$
D. $4$,$0$

Answer 1

Hint: There is a formula for finding the number of radial nodes and also for nodal planes by using the Azimuthal quantum number. Radial node is a sphere shaped surface where the chance of finding an electron is zero. The number of radial nodes increases depending on the principle quantum number (n). Angular nodes are also known as nodal planes. Angular node is a plane that is passing via the nucleus. Angular node is equal to the azimuthal quantum number (l).

Complete step by step answer:
Number of Radial nodes can be found by:
$ \Rightarrow $ $ = n - l - 1$
where n is given in the question which is equal to $4$ and l is equal to $l = 1$$1$
So,
$\begin{gathered}
 n = 4 \\
 l = 1 \\
\end{gathered} $
$ \Rightarrow $ No. of radial nodes $ = 4 - 1 - 1 = 2$
Number of nodal planes = Azimuthal Quantum Number (l)
As $l = 1$
Therefore Number of nodal planes is equal to $1$

Hence, Option B is correct.

Additional Information:
- Nodal planes are regions near atomic nuclei where the chance of finding electrons is zero. The coordinates of these planes are known by solving the Schrödinger wave equation for atoms or molecules to get familiar with the shape of atomic and molecular orbitals.
- An orbital is a three dimensional information of the most likely location of an electron near an atom. Orbital, however in chemistry and physics, is a mathematical expression, known as a wave function, which best describes properties characteristic of not more than two electrons in the vicinity of an atomic nucleus or of a system of nuclei as in a molecule.

Note:
The azimuthal quantum number is generally a quantum number for an atomic orbital that finds its orbital angular momentum and also describes the shape of the orbital. Formula should be known which is very simple for finding the number of radial nodes as well as nodal planes which will help in solving the question.