Content area
Full Text
Introduction and Theory
The first allowed absorption transition of helium (to ls2p ^sup 1^P) lies at 171,129 cm^sup -1^ (58.4 nm) in the vacuum UV and cannot easily be observed in an undergraduate laboratory. However, if students are given the frequency of this transition, they can combine it with measurements on the visible emission spectrum of helium to estimate the ionization energy of this two-electron atom. The extrapolation to the ionization limit takes advantage of the fact that some of the observed transitions can be analyzed quite accurately by the Bohr equation, which treats the excited levels as one-electron systems.
Since two-electron excitations of helium lie above the ionization level, only singly excited levels appear in its spectrum. Similarly to hydrogen, the visible emissions of helium terminate on the n = 2 level. The helium spectrum is more complicated, however, since in a two-electron system there is splitting between s, p, d, ... configurations, due to differing penetration of the outer electron into the ls orbital. In addition, further complications are introduced by the presence of both singlet and triplet levels, as can be seen in an energylevel diagram for the helium atom (1). Nevertheless, some transitions are well described by one-electron theory (i.e., the Bohr equation), in which, for a multi-electron system, the concept of an effective nuclear charge, Z^sub eff^, is incorporated.
where omega^sub n^ is the wavenumber of the transition, epsilon^sub n^ and epsilon^sub 2^ are the energies of the upper and lower levels of the transition, n is the principal quantum number of the excited electron in the upper state, h is Planck's constant, and c is the velocity of light. The Rydberg constant for helium is
and R^sub H^ is that for hydrogen, with mu^sub He^ and mu^sub H^ being the reduced masses of these...