Sankalp NEET Full Test-2 Question-51 Solution

Question 51: The relation between \mathrm{n}_{\mathrm{m}},\left(\mathrm{n}_{\mathrm{m}}=\right. the number of permissible values of magnetic quantum number (m)) for a given value of azimuthal quantum number ( l ), is

(1) \mathrm{n}_{\mathrm{m}}=2 l^{2}+1

(2) \mathrm{n}_{\mathrm{m}}=l+2

(3) l=\frac{n_{m}-1}{2}

(4) l=2 n_{m}+1

Answer: Option (3)

Explanation:

For a given value of azimuthal quantum number l, the magnetic quantum number m can have values ranging from -l to +l, including zero.

Thus, the total number of permissible values of the magnetic quantum number is:

n_m = 2l + 1

Rearranging this relation to express l in terms of n_m, we get:

l = \frac{n_m - 1}{2}

This relation matches Option (3).

Hence, the correct answer is Option (3).