Question

The number of radial nodes of 3s, 3p and 3d electrons are, respectively.

Answer 1

Hint: an orbital is the place where the electrons are found. Orbitals have various shapes, and these shapes consist of a region where the probability of finding an electron is zero. This region is called a node. There are two types of nodes: angular and radial nodes. These nodes can be calculated through the quantum numbers of the electrons.

Formula used:
Number of radial nodes = $\left( n-\ell -1 \right)$

Complete answer:
The structure of an atom consists of electrons that are placed in certain orbitals. The address of these electrons can be identified through quantum numbers like principle ‘n’, secondary$'\ell '$, magnetic ’m’ and spin’s’. The atomic orbitals consist of a place where the probability of finding an electron is null or zero. These regions are called nodes. They are termed as angular and radial. So, the number of these nodes can be identified through the value of quantum numbers using a formula$\left( n-\ell -1 \right)$for radial nodes.
The numbers of radial nodes are calculated as:
-For 3s orbital,
n = 3
$\ell $= 0
Radial nodes = $\left( n-\ell -1 \right)$
Radial nodes = 3 – 0 – 1
Radial nodes = 2
-For 3p orbital,
n = 3
$\ell $= 1
Radial nodes = $\left( n-\ell -1 \right)$
Radial nodes = 3 – 1 – 1
Radial nodes = 1
-For 3d orbital,
n = 3
$\ell $= 2
Radial nodes = $\left( n-\ell -1 \right)$
Radial nodes = 3 – 2 – 1
Radial nodes = 0
Hence, the number of radial nodes in 3s, 3p and 3d orbitals are 2, 1 and 0 respectively.

Note:
The formula to find angular nodes is$'\ell '$ , while total nodes is (n – 1). The quantum number n that is the principal quantum number tells us the number of shells of an electron. The $'\ell '$quantum number is an azimuthal quantum number that tells us the subshells in which the electron is present and its value can be 0 to (n – 1).