As discussed in Chapter 20, in a more exact solution of the Schrödinger equation for the hydrogen atom, the coordinate system is placed at the center of mass of the atom rather than at the nucleus. In that case, the energy levels for a one-electron atom or ion of nuclear charge Z are given by

where μ is the reduced mass of the atom. The masses of an electron, a proton, and a tritium (³H or T) nucleus are given by 9.1094 × 10^ˆ’31kg, 1.6726 × 10^ˆ’27 kg, and 5.0074 × 10^ˆ’27 kg, respectively. Calculate the frequency of the n = 1 †’ n = 4 transition in H and T to five significant figures. Which of the transitions, 1s †’ 4s, 1s †’ 4 p, or 1s †’ 4d, could the frequencies correspond to?

Transcribed Image Text:

4 z?ue* E. En 32negh'n 2,2422