The energy of an electron in the first Bohr orbit of $H$-atom is $-13.6 \ eV$. The possible energy value of an electron in the first excited state of $Li^{2+}$ is (in $eV$)

The ratio of the velocity of an electron in the ground state of a hydrogen atom to its velocity in the second excited state of a $He^{+}$ ion is:

Supposing the electron is present in the $4^{th}$ energy level of $H$ atom. When the electron returns to the ground state,the possible transitions would be:

The difference between the radii of $3^{rd}$ and $2^{nd}$ orbit of $H$ atom is $x \text{ pm}$. The difference between the radii of $4^{th}$ and $3^{rd}$ orbit of $Li^{2+}$ ion is $y \text{ pm}$. The ratio $y:x$ is equal to:

The $\alpha$-particle scattering experiment of Rutherford concluded that

The emission spectrum of a gaseous atom is line-based and not continuous. Why?