Question

Select the correct statement(s):

• A. Radial function [R(r)] a part of wave function is dependent on quantum number n only
  
• B. Angular function depends only on the direction and is independent to the distance from the nucleus
• C. ${\psi }^2(r,\theta ,\varphi )$ is hte probability density of finding the electron at a particular point in space
• D. Radial distribution function $\left(4\pi r^2{R}^2\right)$ gives the probability of the electron being present at a distance r from the nucleus

Answer 1

Answer: (B), (D)

The correct options are
B Angular function depends only on the direction and is independent to the distance from the nucleus
D Radial distribution function $\left(4\pi r^2{R}^2\right)$ gives the probability of the electron being present at a distance r from the nucleus

(a) 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. Hence, option a is incorrect.
(b) The electronic angular wavefunction is one spatial component of the electronic Schrodinger wave equation, which describes the motion of an electron. It depends on angular variables, $\theta$ and $\varphi$, and describes the direction of hte orbital that the electron may occupy. Thus, it depends only on the direction and is independent to the distance from the nucleus.
(c) Probability density of finding an electron at a particular point in space can be given as: ${\psi }^2(r,\theta ,\varphi )$
(d) Radial distribution function $\left(4\pi r^2{R}^2\right)$ gives the probability of the electron being present at a distance r from the nucleus.