Wave number of a spectral line for a given transition is $y \ cm^{-1}$ for $He^{+}$,then its value for $Li^{2+}$ for the same transition is

The radii of two of the first four Bohr’s orbits of the hydrogen atom are in the ratio $1 : 4$. The energy difference between them may be

The energy of the electron in the first orbit of $He^{+}$ is $-871.6 \times 10^{-20} \ J$. The energy of the electron in the first orbit of hydrogen would be

Lifetimes of the molecules in the excited states are often measured by using pulsed radiation source of duration nearly in the nanosecond range. If the radiation source has the duration of $2 \, ns$ and the number of photons emitted during the pulse source is $2.5 \times 10^{15}$,calculate the energy of the source.

The frequency of a certain line of the Lyman series of the atomic spectrum of the $H$ atom satisfies the following conditions:
$(i)$ It is the sum of the frequency of another Lyman line and a Balmer line.
$(ii)$ It is the sum of the frequency of a certain line,a Lyman line,and a Paschen line.
$(iii)$ It is the sum of the frequency of a Lyman and a Paschen line but no Brackett line.
To what transition does this frequency correspond?

The ratio of the wavelengths of the light absorbed by a Hydrogen atom when it undergoes $n=2 \rightarrow n=3$ and $n=4 \rightarrow n=6$ transitions, respectively, is