Match the spectral lines given in List-$I$ with their corresponding lower energy transitions given in List-$II$.

List-$I$	List-$II$
$(1)$ Lyman	$(A)$ $n = 5 \to n = 4$
$(2)$ Paschen	$(B)$ $n = 3 \to n = 2$
$(3)$ Brackett	$(C)$ $n = 6 \to n = 5$
$(4)$ Balmer	$(D)$ $n = 4 \to n = 3$
	$(E)$ $n = 7 \to n = 6$

The energy of an electron in the first Bohr orbit of $H$ atom is $-13.6 \ eV$. The possible energy value$(s)$ of the excited state$(s)$ for electrons in Bohr orbits of the hydrogen atom is(are) $............ \ eV$.

If the potential energy of an electron in the second orbit of $He^+$ is $-27.2 \, eV$,then calculate the double value of the energy of the first excited state of a hydrogen atom in $eV$.

State whether the following statements are true or false:
$(i)$ In Rutherford's atomic model,the Coulombic forces between the nucleus and electrons are mathematically similar to the gravitational forces $F = G \frac{m_1 m_2}{r^2}$.
$(ii)$ Out of every $20000$ $\alpha$-particles,$\sim 10$ particles bounce back after hitting the gold foil.
$(iii)$ In Rutherford's experiment,a zinc sulfide $(ZnS)$ fluorescent screen is placed around the gold foil.
$(iv)$ Rutherford's $\alpha$-particle scattering experiment is related to the size of the atomic nucleus.

The energy of the first (lowest) Balmer line of the $H$ atom is $x \ J$. The energy (in $J$) of the second Balmer line of the $H$ atom is:

The ionization enthalpy of a hydrogen atom is $1.312 \times 10^6 \ J \ mol^{-1}$. The energy required to excite the electron in the atom from $n= 1$ to $n= 2$ is