JEE Main 2023 — Structure Of Atom Question with Solution

Radial nodes in an atomic orbital are areas where the probability of finding an electron is zero. The number of radial nodes in an orbital is given by the formula:

$\text{number of radial nodes}=n-l-1$

where $n$ is the principal quantum number and $l$ is the azimuthal quantum number. The azimuthal quantum number ($l$) can have values from 0 to $n-1$, and it determines the shape of the orbital (s, p, d, f, etc.). For an s orbital, $l=0$; for a p orbital, $l=1$; for a d orbital, $l=2$; and so on.

Let's calculate the number of radial nodes for each given orbital:

1. 7s: $n=7$, $l=0$, so the number of radial nodes is $7-0-1=6$, not 5.
2. 7p: $n=7$, $l=1$, so the number of radial nodes is $7-1-1=5$.
3. 6s: $n=6$, $l=0$, so the number of radial nodes is $6-0-1=5$.
4. 8p: $n=8$, $l=1$, so the number of radial nodes is $8-1-1=6$, not 5.
5. 8d: $n=8$, $l=2$, so the number of radial nodes is $8-2-1=5$.

Therefore, the orbitals with 5 radial nodes are 7p, 6s, and 8d, so there are 3 such orbitals.