Question

Number of radial and angular nodes in $3p$-orbitals respectively are:
A.$1,1$
B.$2,1$
C.$1,2$
D.$2,2$

Answer 1

To find the number of radials and angular nodes in $3p$-orbitals we should have some knowledge about orbitals and their representations. We should have a clear understanding of nodes and their types.

Formula Used:
Number of radial nodes
Radial nodes $= n - l - 1$
Number of angular nodes
Angular nodes $= l$
Where $n$ represents the principal quantum number,
$l$ represents the azimuthal quantum number.

Complete step by step answer:
First, we will understand the basic terms given in the questions. First, we will understand about nodes. Node is a point or plane where electron density or probability of finding an electron is zero.
There are two nodes: radial nodes and angular nodes. A radial node is a spherical node that occurs when the radial wave function for an atomic orbital is equal to zero or changes sign.
Angular node is the region where the angular wave function is zero. These are flat nodes rather than spherical.
Now we will calculate the nodes in $3p$-orbitals. So first we will calculate the radial node. We have given $3p$-orbitals. For the $3p$-orbital, principal quantum number $n = 3$ and the value of azimuthal quantum number $l = 1$ for p-orbital. Now using the formula for the radial node,
Radial nodes $= n - l - 1$, substituting the values of principal and azimuthal quantum number. We get,
Radial nodes $= n - l - 1 = 3 - 1 - 1$
$\Rightarrow$ Radial nodes$= 1$
Now similarly we will calculate the number of angular nodes using its formula. Again for $3p$-orbital we have the principal quantum number $n = 3$ and the value of azimuthal quantum number $l = 1$ for p-orbital. We know that the number of angular nodes is equal to the azimuthal quantum number.
Angular nodes $= l = 1$
We have calculated Radial nodes $= 1$ and Angular nodes $= 1$

Therefore, the correct option is (A).

Note:
The value of the azimuthal quantum number for orbitals is as follows: $l(s) = 0,l(p) = 1,l(d) = 2,l(f) = 3$
We can easily calculate the total number of nodes using the formula $T = n - 1$. For example, for $3p$-orbital we have $n = 3$. Now using the equation we get $T = n - 1 = 3 - 1 = 2$. So total nodes are $2$.