${\mathrm{He}}^{+}$ ions are in an excited state from where maximum $6$ types of photons can be emitted. If $\mathrm{E}$ is the separation energy of ${\mathrm{He}}^{+}$ from this excited state, then how many times of energy $\mathrm{E}$ is required to ionise hydrogen atom?

For a beam of radiation coming out from a sample of ${\mathrm{He}}^{+}$ ions the following energy level diagram was observed (The beam only had photons corresponding to these transitions). If the above beam of radiations is used to excite a sample of $\mathrm{H}$-atoms in the ground state, then find the wavelengths of the photons subsequently emitted by the $\mathrm{H}$-atoms.