In the hydrogen spectrum,if an electron transitions from the $6^{th}$ orbit to the $3^{rd}$ orbit,what is the total number of spectral lines produced?

If the first ionization energy of $H$ atom is $13.6 \ eV,$ then the second ionization energy of $He$ atom is (in $eV$)

The correct representation of the wavelength-intensity relationship of an ideal black body radiation at two different temperatures $T_{1}$ and $T_{2}$ (where $T_{2} > T_{1}$) is:

What is the energy (in $J$ atom$^{-1}$) required for the following process?
$Li^{2+}(g) \to Li^{3+}(g) + e^-$
(Take the ionization energy for the $H$ atom in the ground state as $2.18 \times 10^{-18}$ $J$ atom$^{-1}$)

The difference between the radii of $3^{rd}$ and $4^{th}$ orbits of $Li^{2+}$ is $\Delta R_{1}$. The difference between the radii of $3^{rd}$ and $4^{th}$ orbits of $He^{+}$ is $\Delta R_{2}$. Ratio $\Delta R_{1} : \Delta R_{2}$ is :

If the Thomson model of the atom was correct,then the result of Rutherford's gold foil experiment would have been: