Question

The radial part of wave function depends on the quantum numbers:
The question has multiple correct options
A. n
B. l
C. l, m$_{l}$
D. n only

Answer 1

Hint: The question will be solved on the basis of the solutions in consideration with the Schrodinger’s equation for the atomic orbitals. Identify the terms n, l and m$_{l}$; and the connection with the radial part of wave function could be known.

Complete step by step answer:
* First, we will define the radial wave function. Radial wave functions are considered in the solutions of Schrodinger equation as mentioned.
* We can say that it is defined in terms of the spherical coordinates, one spherical coordinate depicts the distance from the central of the nucleus, the second coordinate represents angle to that of the positive axis i.e. z-axis.
* Now, the third one represents the angle to that of angle in the xy-plane i.e. positive x-axis.
* If we talk about the mentioned options; n represents the principal quantum number i.e. 1, 2, 3, …..so on.
* The l represents the azimuthal quantum number i.e. 0, 1, …, n-1.
* Now, the next we have a magnetic quantum number (m$_{l}$), i.e. –l, …-2, -1, 0, 1, ..l.
* The radial wave function shows its dependence on principal quantum number, and the azimuthal quantum number, as it relates to the position of an electron at a specific point.
* In the last, we can conclude that the radial part of wave function depends on the quantum numbers n, and l.
Hence, the correct option is (A), and (B).

Note: Don’t get confused between the radial wave function, and the angular wave function. We already discussed the dependence of radial wave functions. The angular wave function depends upon azimuthal quantum number, and the magnetic quantum number. Also, Principal quantum number helps in determining the most probable distance and energy of an electron whereas the significance of azimuthal quantum number is in determining the shape of the orbital and its angular momentum.