Question

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

Answer 1

Hint: There are two types of nodes in an orbital, angular, and radial node. Radial nodes are the spherical regions where the probability of finding an electron is zero. This spherical region has a fixed radius. It depends on quantum numbers.
Formula used: Radial node$ = n - l - 1$
Where $n$ is the principal quantum number and $l$ is the azimuthal quantum number.

Complete answer:
As we know, the radial node is a spherical region where the probability of finding an electron is zero. It depends upon the principal quantum number and azimuthal quantum number. The principal quantum number resembles the shell number of the atom. It is represented by $n$. The value of this quantum number is always greater than or equal to $1$. The azimuthal quantum number is also called the orbital angular momentum quantum number. This quantum number describes the shape of the given orbital. It is represented by by $l$. For $p$ orbital its value is$1$. So let’s calculate the number of radial nodes in $3p$ orbital. Formula to calculate the number of radial nodes is:
Radial node$ = n - l - 1$
We can clearly see for $3p$ orbital value of the principal quantum number is $3$ as it is representing shell number. Substituting values of $n$ and $l$ we get,
Radial node$ = 3 - 1 - 1$
Radial node$ = 1$

So the answer to this question is option D that is $1$.

Additional information:
There are two more quantum numbers that are magnetic quantum numbers and spin quantum numbers. The magnetic quantum number describes the orientation of orbitals in a subshell. It is represented by $m$. It varies from $ + l$ to $ - l$. The spin quantum number is independent of all other quantum numbers. It represents the spin of an electron. It is represented by ${m_s}$.


Note:
Like radial nodes, there exist angular nodes. The angular node is the region where the angular wave function is zero. In the case of $p$ orbitals angular nodes are planes but are not always a plane. The number of angular nodes is equal to the azimuthal quantum number that is $l$.