First ionization energy of two electron atoms calculation is shown on p266 (p292 in the reader app) with a table showing agreement with experiment for many 2-electron atoms on p269 (p296 in reader app).
I think it's an interesting method to use a classical model to aproximate atoms, and I surprised that it gives very close results, but I think at the end it's like the Bohr atom, that works in simple cases but fails in the complicated ones. I'll try to think an example where the quantum mechanics effects are big enough to cause a problem.