PHYSICS · Multi-part · A Level · Physics · Particles and radiation · Particles and radiation
Problem
The energy levels of singly ionised helium (He+, atomic number Z=2) can be approximated by En=−54.4eV/n2. A single He+ ion is excited to the n=6 level, after which it is allowed to relax radiatively without external perturbations.
(a) Derive an algebraic expression for the photon energy, in electronvolts, emitted during a transition from an initial level ni to a lower level nf.
(b) Enumerate every distinct transition possible as the ion returns to the ground state and calculate the wavelength of the photon produced in each transition.
(c) Identify which, if any, of the calculated wavelengths lie in the ultraviolet portion of the spectrum (λ<400nm). Provide numerical support for your answer.
(d) Suppose each allowed transition has an equal probability of occurring at each step of a cascade. Qualitatively discuss how this assumption would influence the relative intensities of the spectral lines you found in part (b).