PYQ NEET- Structure Of Atom L-2

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

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

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

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 $(l)$ $$ \begin{aligned} & \Rightarrow \mathrm{n}{\mathrm{m}}=2 \ell+1 \ & \Rightarrow \ell=\frac{\mathrm{n}{\mathrm{m}}-1}{2} \end{aligned} $$