Biomedical Engineering Reference
In-Depth Information
greater than the energies associated with the valence electrons that are involved in
chemical reactions. This factor characterizes the enormous difference in the en-
ergy released when an atom undergoes a nuclear transformation as compared with
a chemical reaction.
The energy associated with exothermic nuclear reactions comes from the con-
version of mass into energy. If the mass loss is
M
, then the energy released,
Q
,
is given by Einstein's relation,
Q
=
M
)
c
2
, where
c
is the velocity of light. In this
section we discuss the energetics of nuclear transformations.
We first establish the quantitative relationship between atomic mass units
(AMU) and energy (MeV). By definition, the
12
C atom has a mass of exactly
12 AMU. Since its gram atomic weight is 12 g, it follows that
(
10
23
)
10
-24
g
10
-27
kg.
1AMU
=
1/(6.02
×
=
1.66
×
=
1.66
×
(3.4)
Using the Einstein relation and
c
= 3 × 10
8
ms
-1
,weobtain
10
-27
)(3
10
8
)
2
1AMU
=
(1.66
×
×
10
-10
J
=
1.49
×
(3.5)
10
-10
J
1.49
×
=
10
-13
JMeV
-1
=
931 MeV.
(3.6)
1.6
×
More precisely, 1 AMU
=
931.49 MeV.
We now consider one of the simplest nuclear reactions, the absorption of a ther-
mal neutron by a hydrogen atom, accompanied by emission of a gamma ray. This
reaction, which is very important for understanding the thermal-neutron dose to
the body, can be represented by writing
1
0
n+
1
H
2
1
H+
0
γ
→
,
(3.7)
the photon having zero charge and mass. The reaction can also be designated
1
1
H
(n,
)
1
H. To find the energy released, we compare the total masses on both sides
of the arrow. Appendix D contains data on nuclides which we shall frequently use.
The atomic weight
M
of a nuclide of mass number
A
can be found from the mass
difference,
, given in column 3. The quantity
=
γ
M
-
A
gives the difference be-
tween the nuclide's atomic weight and its atomic mass number, expressed in MeV.
(By definition,
= 0
for the
12
C atom.) Since we are interested only in energy dif-
ferences in the reaction (3.7), we obtain the energy released,
Q
, directly from the
values of
, without having to calculate the actual masses of the neutron and indi-
vidual atoms. Adding the
values for
0
nand
1
H and subtracting that for
1
H, we
find
(3.8)
Q
=
8.0714 + 7.2890 - 13.1359
=
2.2245 MeV.
This energy appears as a gamma photon emitted when the capture takes place (the
thermal neutron has negligible kinetic energy).
