Biomedical Engineering Reference
In-Depth Information
Solution
This nuclide decays by
+
emission (81.8%) and EC (18.2%) into
2
12
Mg. The energy
release for EC with a transition to the daughter ground state is, from the
values,
β
Q
EC
=
-12.211 + 16.214
=
4.003 MeV.
(3.45)
Here we have neglected the small binding energy of the atomic electron. The corre-
sponding value for
+
decay to the ground state is
Q
β
+
2.981 MeV.
A 1.809-MeV gamma photon is emitted with 100% frequency, and so we can assume
that both EC and
β
=
4.003 - 1.022
=
+
decay modes proceed via an excited daughter state of this energy.
Adding this to the maximum
β
β
+
energy, we have 1.809 + 1.174 = 2.983 MeV =
Q
β
+
.
Therefore, the positron decay occurs as shown in Fig. 3.13(a). Its 81.8% frequency
accounts for the annihilation photons listed with 164% frequency in Appendix D.
The other 18.2% of the decays via EC also go through the level at 1.809 MeV. An ad-
ditional photon of energy 1.130 MeV and frequency 2.5% is listed in Appendix D.
This can arise if a fraction of the EC transformations go to a level with energy
1.809 + 1.130
2.939 MeV above ground. The complete decay scheme is shown in
Fig. 3.13(b). (Some small inconsistencies result from round-off.)
=
Fig. 3.13
Decay scheme of
2
13
Al (see example in text).
