Find the quantum number $n$ corresponding to the excited state of ${\mathrm{He}}^{+} \mathrm{ion},$ if on transition to the ground state that ion emits two photons in succession with wave lengths $108.5 \mathrm{and} 30.4 \mathrm{nm}.$

A stationary hydrogen atom emits a photon corresponding to first line of the Lyman series. What velocity does the atom acquire?

From the condition of the foregoing problem, find how much $($in $\%)$ the energy of the emitted photon differs from the energy of the corresponding transition in a hydrogen atom.

Consider a gas consisting ${\mathrm{Li}}^{2+}$ (which is hydrogen like ion).

(a) Find the wavelength of radiation required to excite the electron in ${\mathrm{Li}}^{2+}$ from $n=1$ and $n=3.$(Ionisation energy of the hydrogen atom equals $13.6 \mathrm{eV}$).

(b) How many spectral lines are observed in the emission spectrum of the above excited system?