1. Chapter 29
Nuclear Physics

2. Properties of Nuclei
All nuclei are composed of protons and neutrons (exception: ordinary hydrogen)
Nucleon is a generic term used to refer to either a proton or a neutron
The atomic number, Z, equals the number of protons in the nucleus
The neutron number, N, is the number of neutrons in the nucleus
The mass number (not the same as the mass), A, is the number of nucleons in the nucleus: A = Z + N

3. Properties of Nuclei Symbol: X is the chemical symbol of the element
Example:
Mass number is 27; atomic number is 13; contains 13 protons and 14 = 27 – 13 neutrons
The Z may be omitted since the element can be used to determine Z
The nuclei of all atoms of a particular element must contain the same number of protons

4. Properties of Nuclei
The nuclei may contain varying numbers of neutrons
Isotopes of an element have the same Z but differing N and A values. For example:
The proton has a single positive charge, +e (e = x C)
The electron has a single negative charge, -e
The neutron has no charge, which makes it difficult to detect

5. Mass
It is convenient to express masses using unified mass units, u, based on definition that the mass of one atom of C-12 is exactly 12 u:
1 u = x kg
Masses
Particle kg u
Proton
x 10-27
Neutron
x 10-27
Electron
9.109 x 10-31
5.486x10-4

6. The Size of the Nucleus
From scattering experiments, Rutherford found an expression for how close an alpha particle moving toward the nucleus can come before being turned around by the Coulomb force
The KE of the particle must be completely converted to PE
d gives an upper limit for the size
of the nucleus (e.g., for gold,
d = 3.2 x m and for silver,
d = 2 x m)

7. The Size of the Nucleus
Such small lengths are often expressed in femtometers where 1 fm = m Also called a fermi
Since the time of Rutherford, many other experiments have concluded that most nuclei are approximately spherical with the average radius of
ro = 1.2 x m
Enrico Fermi
1901 – 1954

8. Chapter 29 Problem 7
(a) Find the speed an alpha particle requires to come within 3.2 × 10−14 m of a gold nucleus. (b) Find the energy of the alpha particle in MeV.

9. Nuclear Stability
There are very large repulsive electrostatic forces between protons
These forces should cause the nucleus to fly apart
The nuclei are stable because of the presence of another, short-range force, called the nuclear force
This is an attractive force that acts between all nuclear particles
The nuclear attractive force is stronger than the Coulomb repulsive force at the short ranges within the nucleus

10. Nuclear Stability Light nuclei are most stable if N = Z
Heavy nuclei are most stable when N > Z
As the number of protons increase, the Coulomb force increases and so more nucleons are needed to keep the nucleus stable
No nuclei are stable when Z > 83

11. Radioactivity Radioactivity is the spontaneous emission of radiation
Radioactivity is the result of the decay (disintegration) of unstable nuclei
Three types of radiation can be emitted
1) Alpha particles: 4He nuclei)
2) Beta particles: either electrons or positrons (a positron is the antiparticle of the electron, similar to the electron except its charge is +e)
3) Gamma rays: high energy photons

12. Penetrating Ability of Particles
Alpha particles: barely penetrate a piece of paper
Beta particles: can penetrate a few mm of aluminum
Gamma rays: can penetrate several cm of lead

13. The Decay Constant
The number of particles that decay in a given time is proportional to the total number of particles in a radioactive sample
ΔN = - λ N Δt
λ: the decay constant; determines the rate at which the material will decay
The decay rate or activity, R, of a sample is defined as the number of decays per second

14. Decay Curve N = No e- λt The decay curve follows the equation
Another useful parameter is the half-life defined as the time it takes for half of any given number of radioactive nuclei to decay

15. Decay Curve

16. Units
The unit of activity, R, is the Curie, Ci: 1 Ci = 3.7 x 1010 decays/second
The most commonly used units of activity are the mCi and the µCi
The SI unit of activity is the Becquerel, Bq: 1 Bq = 1 decay/second (therefore, 1 Ci = 3.7 x 1010 Bq)
Antoine Henri Becquerel
1852 – 1908
Maria Skłodowska-Curie
1867 – 1934

17. Chapter 29 Problem 24
A building has become accidentally contaminated with radioactivity. The longest-lived material in the building is strontium-90. (The atomic mass of is ) If the building initially contained 5.0 kg of this substance, and the safe level is less than 10.0 counts/min, how long will the building be unsafe?

18. Decay – General Rules
When one element changes into another element, the process is called spontaneous decay or transmutation
The sum of the mass numbers, A, must be the same on both sides of the equation
The sum of the atomic numbers, Z, must be the same on both sides of the equation
Conservation of mass-energy and conservation of momentum must hold

19. Alpha Decay
When a nucleus emits an alpha particle it loses two protons and two neutrons (N decreases by 2; Z decreases by 2; A decreases by 4)
Symbolically
X: parent nucleus; Y: daughter nucleus
Example: decay of 226 Ra (half life is
1600 years)
Excess mass is converted into
kinetic energy
Momentum of the two particles is equal and opposite

20. Beta Decay
During beta decay, the daughter nucleus has the same number of nucleons as the parent, but the atomic number is changed by one
Symbolically:
The emission of the electron is from the nucleus, which contains protons and neutrons
The process occurs when a neutron is transformed into a proton and an electron
The energy must be conserved: the energy released in the decay process should almost all go to kinetic energy of the electron (KEmax)

21. Beta Decay
Experiments showed that few electrons had this amount of kinetic energy
To account for this “missing” energy, Pauli proposed the existence of another particle, which Fermi later named the neutrino
Properties of the neutrino:
Zero electrical charge
Mass much smaller than the
electron, probably not zero
Spin of ½
Very weak interaction with
matter

22. Beta Decay Symbolically
 is the symbol for the neutrino; is the symbol for the antineutrino
Therefore, in beta decay, the following pairs of particles are emitted: either an electron and an antineutrino or a positron and a neutrino

23. Gamma Decay
Gamma rays are given off when an excited nucleus “falls” to a lower energy state (similar to the process of electron “jumps” to lower energy states and giving off photons)
The gamma ray photons are very high in energy relative to light
The excited nuclear states result from “jumps” made by a proton or neutron
The excited nuclear states may be the result of violent collision or more likely of an alpha or beta emission

24. Gamma Decay Example of a decay sequence
The first decay is a beta emission
The second step is a gamma emission
The C* indicates the Carbon nucleus is in an excited state
Gamma emission doesn’t change either A or Z

25. Natural Radioactivity
There are unstable nuclei found in nature, which give rise to natural radioactivity
Nuclei produced in the laboratory through nuclear reactions exhibit artificial radioactivity
Three series of natural radioactivity
exist (see table 29.2):
1) Uranium
2) Actinium
3) Thorium (processes through a
series of alpha and beta decays and
ends with a stable isotope of
lead, 208Pb)

26. Nuclear Reactions
Structure of nuclei can be changed by bombarding them with energetic particles
These changes are called nuclear reactions
As with nuclear decays, the atomic numbers and mass numbers must balance on both sides of the equation
E.g., alpha particle colliding with nitrogen:
Balancing the equation allows for the identification of X, so the reaction is

27. Chapter 29 Problem 39
Identify the unknown particles X and X’ in the following nuclear reactions:

28. Answers to Even Numbered Problems
Chapter 28:
Problem 4
ρn/ρa = 8.6 × 1013

29. Answers to Even Numbered Problems
Chapter 28:
Problem 8
1.9 × m
7.4 × m

30. Answers to Even Numbered Problems
Chapter 28:
Problem 10
1.11 MeV/nucleon
7.07 MeV/nucleon
(c) 8.79 MeV/nucleon
(d) 7.57 MeV/nucleon

31. Answers to Even Numbered Problems
Chapter 28:
Problem 18
8.06 d
(b) It is probably 13153I

32. Answers to Even Numbered Problems
Chapter 28:
Problem 20
2.29 g

33. Answers to Even Numbered Problems
Chapter 28:
Problem 38
42He, 42He

34. Answers to Even Numbered Problems
Chapter 28:
Problem 42
105B
–2.79 MeV