Chapter 29: Nuclear Physics

1
My Chapter 29 Lecture
2
Chapter 29 Nuclear Physics

• The Nucleus
• Binding Energy
• Radioactivity
• Half-life
• Biological Effects of Radiation
• Induced Nuclear Reactions
• Fission and Fusion

3
29.1 Nuclear Structure
The atomic nucleus is composed of neutrons and
protons. These particles are called nucleons.
The atoms atomic number (Z) gives the number of
protons in its nucleus. It is the atomic number
that determines an atoms identity.
4
The nucleon number or mass number is A ZN,
where N is the number of neutrons.
Masses of atoms are sometimes give in terms of
atomic mass units. 1u 1.660539?10-27 kg.
5
Atoms of the same element with differing numbers
of neutrons are known as isotopes.
The mass quoted for an atom in the periodic table
is a weighted average over all of the natural
isotopes of that element. The weight factors are
determined by using the relative abundance on
Earth of each isotope.
6
For an atomic nucleus
This implies the density of an atomic nucleus is
independent of A.
As an equality
where r0 1.2?10-15 m 1.2 fm
7
Example (text problem 29.2) Calculate the mass
density of nuclear matter.
Consider a nucleus with one nucleon (A 1).
The density is
8
Example (text problem 29.9) Find the radius and
volume of the nucleus.
The radius is
The volume is
9
29.2 Binding Energy
A nucleus is held together by the strong nuclear
force. This force only acts over distances of a
few fermis.
10
The binding energy (EB) of a nucleus is the
energy that must be supplied to separate it into
individual protons and neutrons.
EB Total energy of Z protons and N neutrons
total energy of nucleus.
11
Total energy of Z protons and N neutrons (mass
of Z protons and N neutrons)c2.
Total energy of nucleus (mass of nucleus)c2.
These can be used to define the mass defect ?m
(mass of Z protons and N neutrons) ? (mass of
nucleus) so that
12
(No Transcript)
13
Nucleons also obey the Pauli Exclusion Principle
such that only two protons (neutrons) can occupy
each proton (neutron) energy level.
Like an atom, a nucleus can be put into an
excited state if it absorbs a photon of the
correct energy. The nucleus can then emit a
photon to go to a lower energy state.
14
(No Transcript)
15
Example (text problem 29.13) (a) Find the
binding energy of the 16O nucleus.
16
Example continued
(b) What is the average binding energy per
nucleon?
17
29.3 Radioactivity
Some nuclei are unstable and decay. These nuclei
are radioactive. A nucleus can emit an alpha
ray, beta ray, or a gamma ray during its decay.
18

• During nuclear reactions
• Charge is conserved.
• The total number of nucleons is constant.
• Energy is conserved.

Define disintegration energy binding energy of
radioactive nucleus ? total binding energy of
products. This is the rest mass energy that can
be converted into other forms of energy.
19
(No Transcript)
20
Alpha rays have been identified as helium nuclei.
The reaction for alpha decay is
Parent nucleus
Alpha particle
Daughter nucleus
21
Example (text problem 29.29) Show that the
spontaneous alpha decay of 19O is not possible.
The reaction is
The mass of the products (including electrons) is
19.01320250u. The mass of 19O is 19.0035787u.
The mass of the products is larger than the
reactant, so this reaction cannot occur
spontaneously.
22
Beta rays have been identified as either
electrons (?-) or positrons (?).
The reaction for beta-minus decay is
The reaction for beta-plus decay is
23
The neutrino and antineutrino have no charge and
are nearly massless. They do not readily
interact with matter.
24
During beta-minus decays, a neutron is converted
into a proton.
During beta-plus decays, a proton is converted
into a neutron.
25
During inverse beta decay (electron capture) a
proton in a nucleus captures an electron. The
reaction is
26
Gamma rays were determined to be high energy
photons.
A gamma ray will be emitted when a nucleus is an
excited state when making a transition to a lower
energy level. For example,
When a nucleus has experienced alpha or beta
decay, it is not always left in the ground state.
27
29.4 Radioactive Decay Rates and Half-Lives
The half-life of a sample of unstable nuclei is
the time it takes for one-half of the sample to
decay. The decay process is quantum mechanical
and is based on probability.
28
Each radioactive nucleus has a probability per
second that it will decay, called the decay
constant.
The number of nuclei that decay in a short time
interval is
29
The decay rate or activity is the number of
radioactive decays that occur in a sample per
unit time.
The unit of activity is the bequerel. 1 Bq 1
decay/sec. Another common unit is the curie. 1
Ci 3.7?1010 Bq.
30
The number of nuclei remaining in a sample having
N0 nuclei at t 0 is
is the mean lifetime of a nucleus.
Note the above expression for N(t) is a way to
determine the number of remaining nuclei only.
It does not tell us which nuclei have decayed.
31
The activity at time t is
where R0 is the activity at t 0.
32
It is common to write the expressions for N(t)
and R(t) in terms of half-life (T1/2).
33
Example (text problem 29.35) Some bones
discovered in a crypt in Guatemala are carbon
dated. The 14C activity is measured to be 0.242
Bq per gram of carbon. Approximately how old are
the bones?
Solve for t
34
29.5 Biological Effects of Radiation
The absorbed dose of ionizing radiation is the
amount of radiation energy absorbed per unit mass
of tissue. Ionizing radiation is radiation with
enough energy to ionize an atom or molecule.
The SI unit of absorbed dose is the Gray. 1 Gy
1 J/kg. Another common unit is the rad
(radiation absorbed dose). 1 rad 0.01 Gy.
35
Different radiation causes different amounts of
biological damage. The biologically equivalent
dose measures the amount of damage caused by
radiation exposure.
Equivalent dose (in sieverts) absorbed dose (in
grays) QF. Equivalent dose (in rem) absorbed
dose (in rads) QF.
QF is a quality factor that is a relative measure
of biological damage (200 keV x-rays have QF 1).
36
The sievert is the SI unit of biologically
equivalent dose. 1 Sy 100 rem.
37
Alpha, beta, and gamma radiation penetrates to
different depths in biological materials.

• Alpha rays are stopped by a few cm of air or
  about 0.02 mm of aluminum.
• Beta-minus can penetrate a few cm into biological
  tissue.
• Gamma ray absorption is based on probability so
  they can penetrate to varying depths.

38
Summary

• The Nucleus (atomic mass numbers)
• Binding Energy
• Radioactive Nuclei
• Alpha, Beta, and Gamma Radiation
• Half-life and Activity
• Absorbed Dose