Question

Angular and spherical nodes in $3s$ are-
A.$1,1$
B.$1,0$
C.$2,0$
D.$0,2$

Answer 1

Hint: Use the formula , the number of angular nodes $ = l$ where l is azimuthal quantum number and the number of spherical nodes $ = n - l - 1$ where n is principal quantum number and l is azimuthal number.

Complete step by step answer:
Nodes are the points where the electron density is zero. There are two types of nodes for a given orbital-
Angular nodes- They are also called nodal planes .They are found in p, d and f-orbital. The s-orbital has no angular nodes.
Radial or spherical nodes- They are also called nodal regions. They are found in $2s,3s,3p,4p,4d,5d$ orbitals.
Here we have to find the numbers of angular and spherical nodes in $3s$
Since here the orbital is s-orbital so it has azimuthal quantum number ($l$)=$0$
And we know that the number of angular nodes$ = l$ where l is azimuthal quantum number
So on putting this value we get,
The number of angular nodes=$0$
Now We know that radial nodes are given by the formula-
The number of spherical nodes $ = n - l - 1$ where n is principal quantum number and l is azimuthal number.
Here $n = 3$ and $l = 0$
So on putting these values in the formula we get,
The number of spherical nodes/radial nodes= $3 - 0 - 1$
On solving we get,
The number of spherical nodes/radial nodes=$2$
Hence the angular and spherical nodes are $0,2$

So the correct option is D.

Note:
-The total number of nodes of any orbital are given by $\left( {n - 1} \right)$ where n is principal quantum number. And we already know that angular nodes are equal to azimuthal quantum number.
-So Radial nodes can also be written as-
Radial nodes=Total number of nodes-Angular nodes
It will give the same formula for the radial nodes.