Biomedical Engineering Reference
In-Depth Information
Fig. 3.4
Nuclear decay scheme of
226
88
Ra.
226
Ra, since the excited state occurs in 5.5% of the total disintegrations and the
0.186 MeV photon is emitted only 3.3% of the time, it follows that internal con-
version occurs in about 2.2% of the total decays. As we show in more detail in
Section 3.6, the energy of the conversion electron is equal to the excited-state en-
ergy (in this case 0.186 MeV) minus the atomic-shell binding energy. The listing in
Appendix D shows one of the e
-
energies to be 0.170 MeV. In addition, since inter-
nal conversion leaves a K- or L-shell vacancy in the daughter atom, one also finds
among the photons emitted the characteristic X rays of Rn. Finally, as noted in the
radiations listed in Appendix D for
226
Ra, various kinds of radiation are emitted
from the radioactive daughters, in this case
222
Rn,
218
Po,
214
Pb,
214
Bi, and
214
Po.
Decay-scheme diagrams, such as that shown in Fig. 3.4 for
226
Ra, conveniently
summarize the nuclear transformations. The two arrows slanting downward to the
left
6)
show the two modes of alpha decay along with the alpha-particle energies and
frequencies. Either changes the nucleus from that of
226
Ra to that of
222
Rn. When
the lower energy particle is emitted, the radon nucleus is left in an excited state with
energy 0.186 MeV above the ground state. (The vertical distances in Fig. 3.4 are
not to scale.) The subsequent gamma ray of this energy, which is emitted almost
immediately, is shown by the vertical wavy line. The frequency 3.3% associated
with this photon emission implies that an internal-conversion electron is emitted
in the other 2.2% of the total number of disintegrations. Radiations not emitted
directly from the nucleus (i.e., the Rn X rays and the internal-conversion electron)
are not shown on such a diagram, which represents the nuclear changes. Relatively
infrequent modes of decay could also be shown, but are not included in Fig. 3.4 (see
Fig. 3.7). (A small round-off error occurs in the energies.)
The most energetic alpha particles are found to come from radionuclides having
relatively short half-lives. An early empirical finding, known as the Geiger-Nuttall
law, implies that there is a linear relationship between the logarithm of the range
R
6 By convention, going left represents a
decrease in
Z
and right, an increase in
Z
.
Photon emission is represented by a vertical
wavy line.
