Identify the $INCORRECT$ statements from the following:
$A.$ Notation ${}_{12}^{24}Mg$ represents $24$ protons and $12$ neutrons.
$B.$ Wavelength of a radiation of frequency $4.5 \times 10^{15} \ s^{-1}$ is $6.7 \times 10^{-8} \ m$.
$C.$ One radiation has wavelength $\lambda_1 = 900 \ nm$ and energy $E_1$. Other radiation has wavelength $\lambda_2 = 300 \ nm$ and energy $E_2$. $E_1 : E_2 = 3 : 1$.
$D.$ Number of photons of light of wavelength $2000 \ pm$ that provides $1 \ J$ of energy is $1.006 \times 10^{16}$.
Choose the correct answer from the options given below:

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:
$[A] (I)(iv)(R)$ $[B] (I)(i)(P)$ $[C] (II)(i)(Q)$ $[D] (I)(i)(S)$

The statement that is $NOT$ correct is:

When the excited electron of a $H$ atom from $n=5$ drops to the ground state,the maximum number of emission lines observed are $.......$

For the given electronic transitions,which of the following statements is correct?

Match the following columns:

Column-$I$	Column-$II$
$(1)$ Photon	$(A)$ Value of $4$ for $N$ shell
$(2)$ Electron	$(B)$ Probability density
$(3)$ $\psi^2$	$(C)$ Always $+$ value
$(4)$ Principal quantum number $(n)$	$(D)$ Represents wavelength and momentum