Biomedical Engineering Reference
In-Depth Information
The process (3.7) is an example of energy release by the fusion of light nuclei.
The binding energy of the deuteron is 2.2245 MeV, which is the energy required to
separate the neutron and proton. As the next example shows, the binding energy
of any nuclide can be calculated from a knowledge of its atomic weight (obtainable
from
) together with the known individual masses of the proton, neutron, and
electron.
Example
Find the binding energy of the nuclide
2
11
Na.
Solution
One can work in terms of either AMU or MeV. The atom consists of 11 protons,
13 neutrons, and 11 electrons. The total mass in AMU of these separate constituents
is, with the help of the data in Appendix A,
11(1.0073) + 13(1.0087) + 11(0.00055)
=
24.199 AMU.
(3.9)
From Appendix D,
= -8.418 MeV gives the difference
M
-
A
. Thus, the mass of
the
2
11
Na nuclide is less than 24 by the amount 8.418 MeV/(931.49 MeV AMU
-1
)
=
0.0090371 AMU. Therefore, the nuclide mass is
M
= 23.991 AMU. Comparison with
(3.9) gives for the binding energy
BE = 24.199 - 23.991 = 0.208 AMU = 194 MeV.
(3.10)
This figure represents the total binding energy of the atom—nucleons plus elec-
trons. However, the electron binding energies are small compared with nuclear
binding, which accounts for essentially all of the 194 MeV. Thus the binding en-
ergy per nucleon in
2
11
Na is 194/24
8.08 MeV. [Had we worked in MeV, rather
than AMU, the data from Appendix A give, in place of (3.9), 2.2541
=
10
4
MeV.
×
10
4
MeV. With
Expressed in MeV,
A
=
24
×
931.49
=
2.2356
×
=
-8.418 MeV
10
4
MeV. Thus the binding energy of the atom is
we have
M
=
A
+
=
2.2348
×
10
4
(2.2541 - 2.2348)
×
=
193 MeV.]
The average binding energy per nucleon is plotted as a function of atomic mass
number in Fig. 3.3. The curve has a broad maximum at about 8.5 MeV from
A
40
to 120.
2)
It then drops off as one goes either to lower or higher
A
. The implication
from this curve is that the
fusion
of light elements releases energy, as does
the fis-
sion
of heavy elements. Both transformations are made exothermic through the
increased average nucleon binding energy that results. The
1
H
(n, γ)
1
H reaction
considered earlier is an example of the release of energy through fusion. With a
few exceptions, the average binding energies for all nuclides fall very nearly on
thesinglecurveshown.Thenuclides
2
He,
1
6
C, and
1
8
O show considerably tighter
=
2 The fact that the average nucleon binding
energy is nearly constant over such a wide
range of
A
is a manifestation of the
saturation property of nuclear forces,
mentioned at the end of Section 2.2.
