Atomic and Molecular Physics
Spring 2015, 1FA558
Department of Physics and Astronomy
Melanie Mucke and Dimitri Arvanitis
Exercise sheet no. 1
Hydrogen and hydrogen-like atoms
To be discussed on Friday, 20/02/2015
1) A hydrogen atom electron is in the 6f state.
a) What are the values of n and l?
b) Compute the energy of the electron.
c) Compute the magnitude of L.
d) Compute the possible values of Lz in this situation.
2) Calculate the electron energies (in eV) for the hydrogen atom with the electron in a 1s-,
2s-, 2p-, 3s-, 3p- or a 3d-orbital. Calculate the wavenumbers and wavelengths of the
radiation from the transitions 3d  2p, 3p  2s and 2p  1s.
3) The spectrum of a one electron ion of a certain element shows the 2s-, 3s- and 4s-orbital
energies at 2 057 972 cm-1, 2 439 156 cm-1 and 2 572 563 cm-1 above the 1s-orbital
energy. Calculate the ionisation energy! Which element is it?
4) A muonic atom, also called mu-mesic atom, is an exotic atom, which can be formed by a
proton and a negative -meson, which has the mass m = 207 me and the charge –e.
How do the energies En of such a muon compare to those of a hydrogen atom?
Hint: You have to use the reduced mass to calculate the energy.
Muon catalyzed fusion is a possible technical application of muonic atoms.
Can you imagine a possible reason why? Give only a short plausibility argument.
5) a) Calculate the expectation value of the radius r for the hydrogen atom for a 2s and for
a 2p orbital.
b) Calculate the radius r for which the radial probability density is maximal for the two
cases.