The electrostatic force of attraction between the electron and the nucleus in a hydrogen atom is given by:

$(i)$ What is the energy of an electron for hydrogen in $J \ atom^{-1}$ and $J \ mol^{-1}$?
$(ii)$ Calculate the energy of this electron per mole for the first transition ($n=1$ to $n=2$).
$(iii)$ Calculate the ionization energy of hydrogen.

Suppose the ionization energy of a hydrogen-like species is $960 \ eV$. The value of the principal quantum number for an energy level of $-60 \ eV$ will be $......$.

$A$ bulb emits light of wavelength $4500 \ \mathring{A}$. The bulb is rated at $150 \ W$ and $8 \ \%$ of the energy is emitted as light. What is the number of photons emitted by the bulb in $1 \ s$?

The energies of an electron in the first orbit of $He^{+}$ and in the third orbit of $Li^{2+}$ in $J$ are respectively:

The wavelength of a particular electron transition for $He^{+}$ is $100 \ nm$. The wavelength (in $\mathring{A}$) of $H$ atom for the same transition is