Page 172 - Radiochemistry and nuclear chemistry

156 Radiochemistry and Nuclear Chemistry

The limitation posed by the recoil phenomenon can be circumvented. If the source and
absorber atoms are fixed in a crystal, the recoil energy may be insufficient to cause bond
breakage. The energy is absorbed as an atomic vibration in the crystal, provided the
quantization of the vibrational states agree exactly with the recoil energy. If not, which is
often the case, the absorber atom stays rigid in the lattice, and the recoil energy is taken
up by the whole crystal. In this case it is necessary to use the mass of the crystal in (4.34)
rather than the mass of a single atom. Under these circumstances the recoil energy becomes
infimtesimally small for the emitting as well as the absorbing atom; this is called recoilless
absorption. The probability for recoilless absorption is improved if the source and absorber
are cooled to low temperatures.
The data of Figure 6.26 were obtained by recoilless absorption in osmium metal
containing 19lOs (source) and Ir metal, both cooled in cryostats. By slowly moving the
source (with velocity v) towards or away from the absorber (see Fig. 6.25), some kinetic
energy AE,f is added or subtracted from the source energy E.7 as "detected" by the absorber
(Doppler effect). The energy and velocity relationship is gwen by the Doppler equation

Z~ /E~/ = v/c (6.29)

The velocity is shown in the Figure, where a value of v of 1 cm s-1 corresponds to 4.3 x
10 -6 eV. The half-value of the v-peak is found to be about 20 x 10 -6 eV, i.e. a factor 4
times higher than calculated by the Heisenberg relationship. This is due to Doppler
broadening of the peak as a consequence of some small atomic vibrations. Although the
M6ssbauer method can be used for measurements of v-line widths, the results are subject
to considerable errors.
One of the most striking uses of the extreme energy resolution obtainable by the
M6ssbauer effect was achieved by R. V. Pound and G. A. Rebka, who measured the
emission of photons in the direction towards the earth's center, and in the opposite direction
from the earth's center. They found that the photon increased its energy by one part in 1016
per meter when falling in the earth's gravitational field. This can be taken as a proof that
the photon of Ehp > 0 does have a mass.
When a "M6ssbauer pair" (like 191Os/Ir, or 57Co/Fe, ll9msn/Sn, 169Er/Tm, etc.) have
source and absorber in different chemical states, the nuclear energy levels differ for the two
M6ssbauer atoms by some amount AEv. By using the same technique as in Figure 6.25,
resonance absorption can be brought about by moving the source with a velocity
corresponding to AE.~. In this manner, a characteristic M6ssbauer spectrum of the
compound (relative to a reference compound) is obtained; the location of the peaks (i.e. the
absorption maxima) with respect to a non-moving source (the isomer shift) is usually given
ill mm s -I .
Figure 6.27 shows the isomer shifts obtained for a number of actinide compounds. The
positions of the isomer shifts show the effect of valence states due to different population
of the 5f orbitals. The different shifts for compounds of the same valence state is a me, asure
of the variation in the covalency of the bonding. The compounds on the loft are metallic.
The shifts reflects the contributions of conduction dectrons to the dectron density at the
nucleus of neptunium.
M6ssbauer spectroscopy is limited to the availability of suitable source, s. About 70
M6ssbauer pairs are now available. The technique provides a useful method for studying