Elements of Modern Physics
118
4. The v = 1.420 × 10
9
s
–1
frequency radiation (known as the 21 cm hydrogen
line) corresponding to the hyperfine transition between the ground state
levels with F = 1 and F = 0, is used to study the distribution and motion (in
terms of Doppler shift) of the hydrogen in interstellar and intergalactic
space.
4.6 EXAMPLES OF ONE-ELECTRON ATOMS
Some examples of one electron atoms are now considered and their special
properties discussed.
Hydrogen
For hydrogen, Z = 1. The l-degeneracy is removed by the relativistic
corrections producing fine structure (Fig. 4.2). The j-degeneracy is removed by
quantum electrodynamic effects (Lamb shift). The spin of the proton doubles
the number of states, while the interaction of the magnetic moment of the proton
with the magnetic field produced by the electron, produces hyperfine structure.
The microwave radiation from transition between the two hyperfine levels of
the ground state, is especially important in producing maser action, in the
investigation of interstellar and extragalactic hydrogen, and as a time standard
in atomic clocks.
Heavier isotopes of hydrogen, such as deuterium and tritium, have spectra
very similar to the hydrogen spectrum, except for small differences due to slightly
different reduced masses (the energy levels are lower for larger reduced
masses). However, the hyperfine structure will be quite different since the spin
and the magnetic moment of their nuclei are quite different from those of the
proton.
Atoms with Z > 1
The singly ionized He (Z = 2) atom and doubly ionized Li (Z = 3) atom,
have energy levels which are larger by a factor of Z
2
. Therefore, their energy
levels with principal quantum numbers n′ = nZ will be similar to those of the
hydrogen atom with principal quantum number n, except for small differences
due to different reduced masses. The fine structures will be significantly
larger, since they vary as Z
4
.
Positronium
Positronium is a bound state of an electron and a positron which has the
same mass as an electron and an equal but opposite charge as an electron (see
Sec. 4.8). They are formed when a beam of positrons is stopped by a gas.
Since the reduced mass for the positronium is m e /2, its energies will be
nearly half those of the hydrogen atom. However, the magnetic moment of a
positron is equal in magnitude to that of the electron, and hence much greater
118
4. The v = 1.420 × 10
9
s
–1
frequency radiation (known as the 21 cm hydrogen
line) corresponding to the hyperfine transition between the ground state
levels with F = 1 and F = 0, is used to study the distribution and motion (in
terms of Doppler shift) of the hydrogen in interstellar and intergalactic
space.
4.6 EXAMPLES OF ONE-ELECTRON ATOMS
Some examples of one electron atoms are now considered and their special
properties discussed.
Hydrogen
For hydrogen, Z = 1. The l-degeneracy is removed by the relativistic
corrections producing fine structure (Fig. 4.2). The j-degeneracy is removed by
quantum electrodynamic effects (Lamb shift). The spin of the proton doubles
the number of states, while the interaction of the magnetic moment of the proton
with the magnetic field produced by the electron, produces hyperfine structure.
The microwave radiation from transition between the two hyperfine levels of
the ground state, is especially important in producing maser action, in the
investigation of interstellar and extragalactic hydrogen, and as a time standard
in atomic clocks.
Heavier isotopes of hydrogen, such as deuterium and tritium, have spectra
very similar to the hydrogen spectrum, except for small differences due to slightly
different reduced masses (the energy levels are lower for larger reduced
masses). However, the hyperfine structure will be quite different since the spin
and the magnetic moment of their nuclei are quite different from those of the
proton.
Atoms with Z > 1
The singly ionized He (Z = 2) atom and doubly ionized Li (Z = 3) atom,
have energy levels which are larger by a factor of Z
2
. Therefore, their energy
levels with principal quantum numbers n′ = nZ will be similar to those of the
hydrogen atom with principal quantum number n, except for small differences
due to different reduced masses. The fine structures will be significantly
larger, since they vary as Z
4
.
Positronium
Positronium is a bound state of an electron and a positron which has the
same mass as an electron and an equal but opposite charge as an electron (see
Sec. 4.8). They are formed when a beam of positrons is stopped by a gas.
Since the reduced mass for the positronium is m e /2, its energies will be
nearly half those of the hydrogen atom. However, the magnetic moment of a
positron is equal in magnitude to that of the electron, and hence much greater