Question

The number of radial nodes for $4p - orbital$ is:
(A) 4
(B) 3
(C) 2
(D) 1

Answer 1

According to the question, firstly we will go through the formula of finding radial number. We should know the azimuthal quantum number and the principal quantum number, these components are involved in finding the radial nodes of orbitals.

Complete step-by-step solution: First, we should know on what basis the orbitals have their nodes like radial nodes.
The number of radial nodes for any orbital is related or dependent to the principal quantum number, $n$ . And, it is also based on the Azimuthal quantum number which has fixed value for each orbital. It is denoted by $l$ .
So, according to the formula of finding the number of radial nodes:
$r = n - l - 1$
here, $r = radial\,node$
$n = principal\,quantum\,no.$
$l = Azimuthal\,quantum\,no.$
So, In $4p - orbital$ :
We already have our principal quantum number that is 4. And, Azimuthal quantum number, $l$ for p-orbital is 1, $l$ is fixed for every orbital such that $s = 0$ , $p = 1$ , $d = 2$ , and $f = 3$ .
$\therefore \,r = 4 - 1 - 1(n = 4;l = 1)$
$\Rightarrow r = 4 - 2$
$\Rightarrow r = 2$ .
So, the number of radial nodes for $4p - orbital$ is 2 .

Hence, the correct option is (C),2 .

Note: A radial node of any orbital is nothing but it’s a spherical surface where the chances of finding an electron is zero that occurs when the radial wavefunction for an atomic orbital is equal to zero or changes sign. And when the principal quantum number will increase then the radial nodes also increase.