Consider the following statements:
$(a)$ Photon is a positively charged nuclear particle
$(b)$ Size of nucleus is very small as compared to the size of atom
$(c)$ Photoelectric effect and diffraction show particle nature of light
$(d)$ Planck's constant has same dimensions as angular momentum
The correct statements is/are:

Match the following laws with their correct statements:

Laws	Statements
$(1)$ Hund's Rule	$(A)$ No two electrons in an atom can have the same set of all four quantum numbers.
$(2)$ Aufbau Principle	$(B)$ Half-filled and fully-filled orbitals have greater stability.
$(3)$ Pauli Exclusion Principle	$(C)$ Electrons prefer to remain unpaired in degenerate orbitals first.
$(4)$ Heisenberg's Uncertainty Principle	$(D)$ It is impossible to determine simultaneously the exact position and exact momentum of an electron.
	$(E)$ In the ground state of atoms,orbitals are filled in the order of increasing energy.

Which one of the following about an electron occupying the $1s$ orbital in a hydrogen atom is incorrect? (Bohr's radius is represented by $a_0$)

Consider the following:
$I$. The electron spin quantum number describes the orientation of the spin of the nucleus with respect to the magnetic field.
$II$. The orbitals represented by the quantum numbers $n=3, l=2, m=+2$ and $n=3, l=2, m=-2$ have the same energy.
$III$. The energy of a photon is directly proportional to wavelength but inversely proportional to wave number.
$IV$. Lyman series of lines appear in ultra-violet region.
The correct statements are:

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:

What is the ratio of time periods in the $3^{rd}$ orbit of $H^{-}$ atom to the $2^{nd}$ orbit of $He^{+}$ ion?