QJEEM23Chb20e: JEE Main 2023 Chemistry - Class 11 JEEM23Chb20e Solution: The number of atomic orbitals from the following having 5…

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.