PYQ NEET- Structure Of Atom L-4

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

A) $l=2 \mathrm{n}_{\mathrm{m}}+1$

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

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

D) $l=\frac{\mathrm{n}_{\mathrm{m}}-1}{2}$

Answer: $l=\frac{\mathrm{n}_{\mathrm{m}}-1}{2}$#

Solution:#

Number of permissible values of magnetic quantum number for a given value of azimuthal quantum $(l)$ $$ \begin{alignedat} & \Rightarrow \mathrm{n}_{\mathrm{m}}=2 \ell+1 \ & \Rightarrow \ell=\frac{\mathrm{n}_m-1}{2} \end{aligned} $$