PHY328 Student Note 2 Part 2

LECTURE NOTE 2 PART 2
Nuclear Properties
2.3 Nuclear Binding Energies
The binding energy, BE, of a nucleus is the energy needed to separate all the nucleons in the
nucleus. That is:
( ) ( ) ( )
The binding energy of a nucleus can be calculated easily since it is equal to the mass defect (or
mass lost) when the nucleus was formed. For a nucleus, , with proton number Z and neutron
number N = A – Z, the mass defect, ∆m, is given by
( ) ( ) ( )
where, is the proton mass, is the neutron mass, and ( ) is the mass of the nucleus
given in atomic mass units. The binding energy of the nucleus is then given as:
( ) ( )
Or,
( ) [ ( ) ( )] ( )
Example 2.3: Calculate the binding energy of the Deuterium nucleus ( ).
Figure 2.2 shows a graph of the binding energy per nucleon, ⁄ , as a function of nuclear mass
number, A, for all known nuclei.
Page 1 of 5
Fig. 2.2: Binding energy per nucleon as a function of the nuclear mass number
Observe that the values of BE/A increases sharply with A for light nuclei and decreases slowly
from about 8.5 MeV to 7.5 MeV beginning with , where it has a maximum. From the
curve, it is observe that from the binding energy BE is approximately proportional to A.
In the light nuclei region, fewer points are observed whose binding energy per nucleon is greater
than the local average: , and . The nuclei and and also lie in the upper
part of the graph. Observe that these nuclei have equal and even proton and neutron numbers.
The initial rise of the BE/A curve indicates that the fusion of two light nuclei produces a nucleus
with greater binding energy per nucleon, and releasing energy.
Another quantity of interest is the separation energy of a nucleon from the nucleus.
Neutron Separation Energy:
( ) ( ) ( )
Page 2 of 5
( ) [ ( ) ( )] ( )
Proton Separation Energy:
( ) ( ) ( )
( ) [ ( ) ( )] ( )
The separation energy can vary from a few MeV to about 20 MeV and depends very much on the
structure of the nucleus. It has been observed that separation energy is greater for nuclei with
even number of neutrons. The plots of the separation energy versus Z or N, shows that at the
values 2, 8, 20, 50, 82, 126, 184, the separation energy changes abruptly. These values are
known as magic numbers.
Example 2.4: Calculate the binding energy of the last neutron in .
2.4 Nuclear Excited States
Like all quantum systems, the nucleus possesses a sequence of excited states, above the ground
state with zero energy. The values of the energy of these states are normally presented in energy
level diagrams that also give the values of spin and parity corresponding to each state. The goal
of the field of nuclear spectroscopy is to observe the possible excited states of all nuclei and to
measure their properties. An example of the energy level diagrams of and is shown in
Figure 2.3:
Page 3 of 5
Fig. 2.3: The energy level spectra of an even-even and odd-odd nucleus.
In Figure 2.3, the numbers on the right of each level are the energies in MeV and the numbers on
the left are the spin and parity of the state. It has been experimentally observed that the
distribution of states varies enormously from nucleus to nucleus. Also, it is a general rule that the
density of states increases rapidly with energy, and forms a continuum at high energies. The
energies of the first excited states are also affected by the presence of a magic number of protons
and neutrons in the nucleus.
2.5 Nuclear Stability
The nuclear excited states discussed in section 2.4 are unstable and decays to a lower energy
state of the same nucleus with the emission of a Gamma ray. The sequence of these transitions
leads normally to the ground state of that nucleus. However, the ground state itself may not be
stable for many nuclides, which can decay into other nuclides by radioactivity. The several
options for the transformation or decay of an unstable nucleus in its ground state will be
discussed in details under the topic of radioactive decay. Figure 2.4 shows the nuclear stability
curve of some nuclei.
Page 4 of 5
Fig. 2.4: The Nuclear Stability Curve
The stability curve shows the distribution in Z and N of the stable nuclides and the known
unstable ones. A greater majority of the unstable nuclides are artificially produced in the
laboratory and only a few exist in nature in significant amounts. The stable nuclei define a band
in Figure 2.4 called the β-stability line. The nuclides below that line have excess neutrons and are
unstable by β- decay. Conversely, the nuclides above the line have an excess of protons and are
unstable by β+ decay. A chart based on the nuclear stability curve that provides more detailed
information about each nucleus, is partially shown in Figure 2.5.
Fig. 2.5: Partial Chart of Nuclides
This chart is known as the Chart of Nuclides. Each cell in the chart of nuclides represents a
nucleus. Observe that the more distant from the line of stability a nuclide is, the more unstable it
is.
Page 5 of 5

PHY328 Student Note 2 Part 2

Uploaded by

Copyright:

Available Formats

PHY328 Student Note 2 Part 2

Uploaded by

Document Information

Copyright

Available Formats

Share this document

Share or Embed Document

Sharing Options

Did you find this document useful?

Is this content inappropriate?

Copyright:

Available Formats

PHY328 Student Note 2 Part 2

Uploaded by

Copyright:

Available Formats

LECTURE NOTE 2 PART 2

2.3 Nuclear Binding Energies

Example 2.3: Calculate the binding energy of the Deuterium nucleus ( ).

Neutron Separation Energy:

Proton Separation Energy:

Example 2.4: Calculate the binding energy of the last neutron in .

2.4 Nuclear Excited States

2.5 Nuclear Stability

Fig. 2.5: Partial Chart of Nuclides

You might also like