Chemistry - Atomic Structure Question with Solution | TestHub

An orbital in a H -atom is associated with the following radial and angular parts of its wave function: $$\begin{gathered} \text{displaylines}\Psi (r)=\frac{1}{9\sqrt{30}}{\left(\frac{\mathrm{Z}}{{\mathrm{a}}_0}\right)}^{3/2}{\sigma }^2{e}^{-\sigma /2}; \\ \Psi (\theta ,\varphi )={\left(\frac{15}{4\pi }\right)}^{1/2}\sin \theta \cos \theta \cos \varphi \end{gathered}$$

Here, $\sigma =\frac{2\mathrm{r}}{{\mathrm{na}}_0},{\mathrm{a}}_0=\frac{{\mathrm{h}}^2}{4{\pi }^2{\mathrm{me}}^2},\theta =$ angle from z -axis, $\varphi =$ angle of component in xy plane with x -axis. If $p_x,p_y\&p_z$ orbitals have been hypothetically assigned m values as $+1,-1$ & 0 respectively and ${\mathrm{d}}_{\mathrm{xy}},{\mathrm{d}}_{\mathrm{yz}}$, $d_{zx},d_{x^2-y^2}\&d_{z^2}$ orbitals have been hypothetically assigned $m$ values as $+2,-2,+1,-1\&0$ respectively, determine value of $(\mathrm{n}+\ell +\mathrm{m})$ for the given orbital.