In general, for any given shell, the s orbitals will be filled preferentially
compared to the p orbitals due to larger shielding experienced by electrons
in the p orbitals. Likewise, the shielding ideal can be applied to argue that
the p orbital is filled before the d orbital for the n=3 and higher shells,
and the d orbital before the f orbital in the n=4 and higher shells. Electrons
will preferentially occupy different p, d, or f orbitals is they are available
before occupying the same orbital. This gives the following trend for increas-
ing energy of orbitals:
1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d...As the number of electrons increases, the detailed interactions between the
electrons become increasingly important in defining the relative energies
of the orbitals. For example, in the transition metals, the electron con-
figuration of chromium is 4s^1 3d^5 rather than the expected 4s^2 3d^4 and
copper has the configuration 4s^1 3d^10 rather than 4s^2 3d^9. The reason for
the configuration of chromium is that by spreading the electrons over five
d orbitals, the unfavorable electron repulsion is decreased. For copper, the
completion of the d orbital provides a more stable configuration than the
nearly complete configuration.
Problems
12.1 Write the potential for the hydrogen atom.
12.2 Calculate the energy of the (a) ground state and (b) first excited state.
12.3 Write the energy of an electron in a 3pxorbital for the hydrogen atom in the Bohr model.
12.4 Calculate the position of the radial node of the 2s orbital.
12.5 Calculate the mean radius of the 1s state.
12.6 Calculate the most probable radius of the 1s orbital.
12.7 List the three quantum numbers for the hydrogen atom and their allowed values.
12.8 Calculate the wavelength of light absorbed for a transition of n=1 to n=3.
12.9 What is the physical interpretation of the three quantum numbers obtained for the
hydrogen atom?
CHAPTER 12 THE HYDROGEN ATOM 267
References
Armstrong, F.A. (2004) Hydrogenases: active site
puzzles and progress. Current Opinion in Chemical
Biology 8 , 133 – 40.
Hoffert, M.I., Caldeira, K., Benford, G. et al. (2002)
Advanced technology paths to global climate sta-
bility: energy for a greenhouse planet. Science 298 ,
981– 7.
US Department of Energy (2003) Report of the Basic
Energy Sciences Workshop on Hydrogen Production,
Storage, and Use. US Department of Energy,
Argonne National Laboratory.
Vignas, P.M., Billoud, B., and Meyer, J. (2001)
Classification and phylogeny of hydrogenases.
FEMS Microbiology Re 9 iews 25 , 455 –501.