The wave function $\psi_{n, l, m_l}$ is a mathematical function whose value depends upon spherical polar coordinates $(r, \theta, \phi)$ of the electron and is characterized by the quantum numbers $n, l$ and $m_l$. Here $r$ is the distance from the nucleus,$\theta$ is the colatitude,and $\phi$ is the azimuth. In the mathematical functions given in the Table,$Z$ is the atomic number and $a_0$ is the Bohr radius.

Column-$I$	Column-$II$	Column-$III$
$I$. $1s$ orbital	$i$. $\psi_{n, l, m_l} \propto (\frac{Z}{a_0})^{3/2} e^{-(Zr/a_0)}$	$P$. (Graph shown)
$II$. $2s$ orbital	$ii$. One radial node	$Q$. Probability density at nucleus $\propto 1/a_0^3$
$III$. $2p_z$ orbital	$iii$. $\psi_{n, l, m_l} \propto (\frac{Z}{a_0})^{5/2} r e^{-(Zr/2a_0)} \cos \theta$	$R$. Probability density is maximum at nucleus
$IV$. $3d_{z^2}$ orbital	$iv$. $xy$-plane is a nodal plane	$S$. Energy needed to excite electron from $n=2$ state to $n=4$ state is $27/32$ times the energy needed to excite electron from $n=2$ state to $n=6$ state

$1$. For the given orbital in Column-$I$,the only $CORRECT$ combination for any hydrogen-like species is:
$[A] (IV)(iv)(R)$ $[B] (II)(ii)(P)$ $[C] (III)(iii)(P)$ $[D] (I)(ii)(S)$
$2$. For $He^{+}$ ion,the only $INCORRECT$ combination is:
$[A] (II)(ii)(Q)$ $[B] (I)(i)(S)$ $[C] (I)(i)(R)$ $[D] (I)(iii)(R)$
$3$. For the hydrogen atom,the only $CORRECT$ combination is:
$[A] (I)(iv)(R)$ $[B] (I)(i)(P)$ $[C] (II)(i)(Q)$ $[D] (I)(i)(S)$

• A
• B
• C
• D