Biomedical Engineering Reference
In-Depth Information
One thus obtains for the alpha-particle energy
MQ
m
+
M
.
1
2
mv
2
(3.18)
E
α
=
=
With the roles of the two masses interchanged, it follows that the recoil energy of
the nucleus is
mQ
m
+
M
.
1
2
MV
2
E
N
=
=
(3.19)
Asacheck,weseethat
E
α
+
E
N
=
Q
. Because of its much smaller mass, the alpha
particle, having the same momentum as the nucleus, has much more energy. For
226
Ra, it follows from (3.14) and (3.18) that
222
4.88
4 + 222
×
E
α
=
= 4.79 MeV.
(3.20)
The radon nucleus recoils with an energy of only 0.09 MeV.
The conservation of momentum and energy, Eqs. (3.15) and (3.16), fixes the en-
ergy of an alpha particle uniquely for given values of
Q
and
M
. Alpha particles
therefore occur with discrete values of energy.
Appendix D gives the principal radiations emitted by various nuclides. We
consider each of those listed for
226
Ra. Two alpha-particle energies are shown:
4.785 MeV, occurring with a frequency of 94.4% of all decays, and 4.602 MeV, oc-
curring 5.5% of the time. The
Q
value for the less frequent alpha particle can be
found from Eq. (3.18):
(
m
+
M
)
E
α
M
226
4.60
222
×
(3.21)
Q
=
=
=
4.68 MeV.
The decay in this case goes to an excited state of the
222
Rn nucleus. Like excited
atomic states, excited nuclear states can decay by photon emission. Photons from
the nucleus are called gamma rays, and their energies are generally in the range
from tens of keV to several MeV. Under the gamma rays listed in Appendix D for
226
Ra we find a 0.186-MeV photon emitted in 3.3% of the decays, in addition to
another that occurs very infrequently (following alpha decay to still another excited
level of higher energy in the daughter nucleus). We conclude that emission of the
higher energy alpha particle
(
E
α
=
4.79
MeV) leaves the daughter
222
Rn nucleus in
its ground state. Emission of the 4.60 MeV alpha particle leaves the nucleus in an
excited state with energy 4.79 - 4.60
0.19 MeV above the ground state. A photon
of this energy can then be emitted from the nucleus, and, indeed, one of energy
0.186 MeV is listed for 3.3% of the decays. As an alternative to photon emission, un-
der certain circumstances an excited nuclear state can decay by ejecting an atomic
electron, usually from the K or L shell. This process, which produces the electrons
listed (e
-
), is called internal conversion, and will be discussed in Section 3.6.
5)
For
=
5
In atoms, an Auger electron can be ejected
from a shell in place of a photon,
accompanying an electronic transition (Sect.
2.11).
