Chemistry - Atomic Structure Question with Solution | TestHub

The wave function, ${\mathrm{\psi }}_{\mathrm{n},\mathrm{ }\mathrm{l},\mathrm{ }{\mathrm{m}}_{\mathrm{l}}}$ is a mathematical function whose value depends upon spherical polar coordinates $\left(\mathrm{r},\mathrm{ }\mathrm{\theta },\mathrm{ }\mathrm{\varphi }\right)$ of the electron and characterized by the quantum numbers $\mathrm{n},\mathrm{ }\mathrm{l}$ and ${\mathrm{m}}_{\mathrm{l}}$ . Here $\mathrm{r}$ is the distance from the nucleus, $\mathrm{\theta }$ is colatitude and $\mathrm{\varphi }$ is azimuth. In the mathematical functions given in the Table, $\mathrm{Z}$is the atomic number and ${\mathrm{a}}_{\mathrm{o}}$ is Bohr radius
 

Column  1	Column  2	Column 3
(I) $1\mathrm{s}$ orbital	(i) ${\mathrm{\psi }}_{\mathrm{n},\mathrm{ }\mathrm{l},\mathrm{ }{\mathrm{m}}_{\mathrm{l}}}\mathrm{ }\propto {\left(\frac{\mathrm{Z}}{{\mathrm{a}}_{\mathrm{o}}}\right)}^{\frac{3}{2}}\mathrm{ }{\mathrm{e}}^{-\left(\frac{\mathrm{Zr}}{{\mathrm{e}}_{\mathrm{o}}}\right)}$	(P)
(II) $2\mathrm{s}$ orbital	(ii) One radial node	(Q) Probability density at the nucleus $\propto \frac{1}{{\mathrm{a}}_{\mathrm{o}}^3}$.
(III) $2{\mathrm{p}}_{\mathrm{z}}$ orbital	(iii) ${\mathrm{\psi }}_{\mathrm{n},\mathrm{ }\mathrm{l},\mathrm{ }{\mathrm{m}}_{\mathrm{l}}}\mathrm{ }\propto {\left(\frac{\mathrm{Z}}{{\mathrm{a}}_{\mathrm{o}}}\right)}^{\frac{5}{2}}{\mathrm{re}}^{-\left(\frac{\mathrm{Zr}}{2{\mathrm{a}}_{\mathrm{o}}}\right)}\cos \mathrm{\theta }$	(R) Probability density is maximum at the nucleus.
(IV) $3{\mathrm{d}}_{\mathrm{z}}^2$ orbital	(iv) $\mathrm{xy}$ -plane is a nodal plane	(S) Energy needed to excite an electron from $\mathrm{n}=2$ state to $\mathrm{n}=4$ state is $\frac{27}{32}$ times the energy needed to excite are electron from $\mathrm{n}=2$ state to $\mathrm{n}=6$ state.

For the given orbital in column 1, the only correct combination for any hydrogen-like species is