1. Chapter 29
Nuclear Physics

2. Milestones in the Development of Nuclear Physics
1896 – the birth of nuclear physics
Becquerel discovered radioactivity in uranium compounds
Rutherford showed the radiation had three types
Alpha (He nucleus)
Beta (electrons)
Gamma (high-energy photons)

3. More Milestones
1911 Rutherford, Geiger and Marsden performed scattering experiments
Established the point mass nature of the nucleus
Nuclear force was a new type of force
1919 Rutherford and coworkers first observed nuclear reactions in which naturally occurring alpha particles bombarded nitrogen nuclei to produce oxygen

4. Milestones, final
1932 Cockcroft and Walton first used artificially accelerated protons to produce nuclear reactions
1932 Chadwick discovered the neutron
1933 the Curies discovered artificial radioactivity
193 Hahn and Strassman discovered nuclear fission
1942 Fermi and collaborators achieved the first controlled nuclear fission reactor

5. Some Properties of Nuclei
All nuclei are composed of protons and neutrons
Exception is ordinary hydrogen with just a proton
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, A, is the number of nucleons in the nucleus
A = Z + N
Nucleon is a generic term used to refer to either a proton or a neutron
The mass number is not the same as the mass

6. Symbolism
X is the chemical symbol of the element
Example:
Mass number is 27
Atomic number is 13
Contains 13 protons
Contains 14 (27 – 13) neutrons
The Z may be omitted since the element can be used to determine Z

7. More Properties
The nuclei of all atoms of a particular element must contain the same number of protons
They may contain varying numbers of neutrons
Isotopes of an element have the same Z but differing N and A values
Example:

8. Charge The proton has a single positive charge, +e
The electron has a single negative charge, -e
The neutron has no charge
Makes it difficult to detect
e = x C

9. Mass It is convenient to use atomic mass units, u, to express masses
1 u = x kg
Based on definition that the mass of one atom of C-12 is exactly 12 u
Mass can also be expressed in MeV/c2
From ER = m c2
1 u = MeV/c2

10. Summary of Masses Masses Particle kg u MeV/c2 Proton 1.6726 x 10-27
938.28
Neutron
x 10-27
939.57
Electron
9.101 x 10-31
5.486x10-4
0.511

11. The Size of the Nucleus
First investigated by Rutherford in scattering experiments
He 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

12. Size of the Nucleus, cont
d gives an upper limit for the size of the nucleus
Rutherford determined that
For gold, he found d = 3.2 x m
For silver, he found d = 2 x m
Such small lengths are often expressed in femtometers where 1 fm = m
Also called a fermi

13. Size of Nucleus, Current
Since the time of Rutherford, many other experiments have concluded the following
Most nuclei are approximately spherical
Average radius is
ro = 1.2 x m

14. Density of Nuclei
The volume of the nucleus (assumed to be spherical) is directly proportional to the total number of nucleons
This suggests that all nuclei have nearly the same density
Nucleons combine to form a nucleus as though they were tightly packed spheres

15. 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

16. Nuclear Stability, cont
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

17. Binding Energy
The total energy of the bound system (the nucleus) is less than the combined energy of the separated nucleons
This difference in energy is called the binding energy of the nucleus
It can be thought of as the amount of energy you need to add to the nucleus to break it apart into separated protons and neutrons

18. Binding Energy per Nucleon

19. Binding Energy Notes
Except for light nuclei, the binding energy is about 8 MeV per nucleon
The curve peaks in the vicinity of A = 60
Nuclei with mass numbers greater than or less than 60 are not as strongly bound as those near the middle of the periodic table
The curve is slowly varying at A > 40
This suggests that the nuclear force saturates
A particular nucleon can interact with only a limited number of other nucleons

20. Radioactivity Radioactivity is the spontaneous emission of radiation
Experiments suggested that radioactivity was the result of the decay, or disintegration, of unstable nuclei

21. Radioactivity – Types Three types of radiation can be emitted
Alpha particles
The particles are 4He nuclei
Beta particles
The particles are either electrons or positrons
A positron is the antiparticle of the electron
It is similar to the electron except its charge is +e
Gamma rays
The “rays” are high energy photons

22. Distinguishing Types of Radiation
The gamma particles carry no charge
The alpha particles are deflected upward
The beta particles are deflected downward
A positron would be deflected upward

23. 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

24. 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 is called the decay constant and 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

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

26. Units The unit of activity, R, is the Curie, Ci
1 Ci = 3.7 x 1010 decays/second
The SI unit of activity is the Becquerel, Bq
1 Bq = 1 decay / second
Therefore, 1 Ci = 3.7 x 1010 Bq
The most commonly used units of activity are the mCi and the µCi

27. What fraction of a radioactive sample has decayed after two half-lives have elapsed? (a) 1/4 (b) 1/2 (c) 3/4 (d) not enough information to say
QUICK QUIZ 29.1

28. QUICK QUIZ 29.1 ANSWER
(c). At the end of the first half-life interval, half of the original sample has decayed and half remains. During the second half-life interval, half of the remaining portion of the sample decays. The total fraction of the sample that has decayed during the two half-lives is:

29. QUICK QUIZ 29.2
The activity of a newly discovered radioactive isotope reduces to 96% of its original value in an interval of 2 hours. What is its half-life? (a) 10.2 h (b) 34.0 h (c) 44.0 h (d) 68.6 h

30. QUICK QUIZ 29.2 ANSWER
(b). If the original activity is R0, the activity remaining after an elapsed time t is R = R0e-λt = R0e-(0.693/T1/2)t . Solving for the half-life yields T1/2 = [-0.693/ln(R/R0)]t. If R = 0.96R0 at t = 2.0 hr, the half-life is: T1/2 = [-0.693/ln(0.96)](2.0 h) = 34 h.

31. 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 is called the parent nucleus
Y is called the daughter nucleus

32. Alpha Decay -- Example Decay of 226 Ra
Half life for this decay is 1600 years
Excess mass is converted into kinetic energy
Momentum of the two particles is equal and opposite

33. 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

34. QUICK QUIZ 29.3
If a nucleus such as 226Ra that is initially at rest undergoes alpha decay, which of the following statements is true? (a) The alpha particle has more kinetic energy than the daughter nucleus. (b) The daughter nucleus has more kinetic energy than the alpha particle. (c) The daughter nucleus and the alpha particle have the same kinetic energy.

35. QUICK QUIZ 29.3 ANSWER
(a). Conservation of momentum requires the momenta of the two fragments be equal in magnitude and oppositely directed. Thus, from KE = p2/2m, the lighter alpha particle has more kinetic energy that the more massive daughter nucleus.

36. Beta Decay
During beta decay, the daughter nucleus has the same number of nucleons as the parent, but the atomic number is one less
Symbolically

37. Beta Decay, cont The emission of the electron is from the nucleus
The nucleus contains protons and neutrons
The process occurs when a neutron is transformed into a proton and an electron
Energy must be conserved

38. Beta Decay – Electron Energy
The energy released in the decay process should almost all go to kinetic energy of the electron
Experiments showed that few electrons had this amount of kinetic energy

39. Neutrino
To account for this “missing” energy, in 1930 Pauli proposed the existence of another particle
Enrico Fermi later named this particle 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

40. Beta Decay – Completed Symbolically  is the symbol for the neutrino
is the symbol for the antineutrino
To summarize, in beta decay, the following pairs of particles are emitted
An electron and an antineutrino
A positron and a neutrino

41. 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 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

42. Gamma Decay – Example 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

43. Uses of Radioactivity Carbon Dating Smoke detectors
Beta decay of 14C is used to date organic samples
The ratio of 14C to 12C is used
Smoke detectors
Ionization type smoke detectors use a radioactive source to ionize the air in a chamber
A voltage and current are maintained
When smoke enters the chamber, the current is decreased and the alarm sounds

44. More Uses of Radioactivity
Radon pollution
Radon is an inert, gaseous element associated with the decay of radium
It is present in uranium mines and in certain types of rocks, bricks, etc that may be used in home building
May also come from the ground itself

45. Natural Radioactivity
Classification of nuclei
Unstable nuclei found in nature
Give rise to natural radioactivity
Nuclei produced in the laboratory through nuclear reactions
Exhibit artificial radioactivity
Three series of natural radioactivity exist
Uranium
Actinium
Thorium

46. Decay Series of 232Th Series starts with 232Th
Processes through a series of alpha and beta decays
Ends with a stable isotope of lead, 208Pb

47. Nuclear Reactions
Structure of nuclei can be changed by bombarding them with energetic particles
The changes are called nuclear reactions
As with nuclear decays, the atomic numbers and mass numbers must balance on both sides of the equation

48. Which of the following are possible reactions?
QUICK QUIZ 29.4
Which of the following are possible reactions?

49. QUICK QUIZ 29.4 ANSWER
(a) and (b). Reactions (a) and (b) both conserve total charge and total mass number as required. Reaction (c) violates conservation of mass number with the sum of the mass numbers being 240 before reaction and being only 223 after reaction.

50. Q Values Energy must also be conserved in nuclear reactions
The energy required to balance a nuclear reaction is called the Q value of the reaction
An exothermic reaction
There is a mass “loss” in the reaction
There is a release of energy
Q is positive
An endothermic reaction
There is a “gain” of mass in the reaction
Energy is needed, in the form of kinetic energy of the incoming particles
Q is negative

51. Threshold Energy
To conserve both momentum and energy, incoming particles must have a minimum amount of kinetic energy, called the threshold energy
m is the mass of the incoming particle
M is the mass of the target particle
If the energy is less than this amount, the reaction cannot occur

52. QUICK QUIZ 29.5
If the Q value of an endothermic reaction is MeV, the minimum kinetic energy needed in the reactant nuclei if the reaction is to occur must be (a) equal to 2.17 MeV, (b) greater than 2.17 MeV, (c) less than 2.17 MeV, or (d) precisely half of 2.17 MeV.

53. QUICK QUIZ 29.5 ANSWER
(b). In an endothermic reaction, the threshold energy exceeds the magnitude of the Q value by a factor of (1+ m/M), where m is the mass of the incident particle and M is the mass of the target nucleus.

54. Radiation Damage in Matter
Radiation absorbed by matter can cause damage
The degree and type of damage depend on many factors
Type and energy of the radiation
Properties of the absorbing matter
Radiation damage in biological organisms is primarily due to ionization effects in cells
Ionization disrupts the normal functioning of the cell

55. Types of Damage
Somatic damage is radiation damage to any cells except reproductive ones
Can lead to cancer at high radiation levels
Can seriously alter the characteristics of specific organisms
Genetic damage affects only reproductive cells
Can lead to defective offspring

56. Units of Radiation Exposure
Roentgen [R] is defined as
That amount of ionizing radiation that will produce 2.08 x 109 ion pairs in 1 cm3 of air under standard conditions
That amount of radiation that deposits 8.76 x 10-3 J of energy into 1 km3 of air
Rad (Radiation Absorbed Dose)
That amount of radiation that deposits 10-2 J of energy into 1 kg of air

57. More Units RBE (Relative Biological Effectiveness)
The number of rad of x-radiation or gamma radiation that produces the same biological damage as 1 rad of the radiation being used
Accounts for type of particle which the rad itself does not
Rem (Roentgen Equivalent in Man)
Defined as the product of the dose in rad and the RBE factor
Dose in rem = dos in rad X RBE

58. Radiation Levels Natural sources – rocks and soil, cosmic rays
Background radiation
About 0.13 rem/yr
Upper limit suggested by US government
0.50 rem/yr
Excludes background and medical exposures
Occupational
5 rem/yr for whole-body radiation
Certain body parts can withstand higher levels
Ingestion or inhalation is most dangerous

59. Applications of Radiation
Sterilization
Radiation has been used to sterilize medical equipment
Used to destroy bacteria, worms and insects in food
Bone, cartilage, and skin used in graphs is often irradiated before grafting

60. Applications of Radiation, cont
Tracing
Radioactive particles can be used to trace chemicals participating in various reactions
Example, 131I to test thyroid action
CAT scans
Computed Axial Tomography
Produces pictures with greater clarity and detail than traditional x-rays

61. Applications of Radiation, final
MRI
Magnetic Resonance Imaging
When a nucleus having a magnetic moment is placed in an external magnetic field, its moment processes about the magnetic field with a frequency that is proportional to the field
Transitions between energy states can be detected electronically

62. Radiation Detectors
A Geiger counter is the most common form of device used to detect radiation
It uses the ionization of a medium as the detection process
When a gamma ray or particle enters the thin window, the gas is ionized
The released electrons trigger a current pulse
The current is detected and triggers a counter or speaker

63. Detectors, 2 Semiconductor Diode Detector Scintillation counter
A reverse biased p-n junction
As a particle passes through the junction, a brief pulse of current is created and measured
Scintillation counter
Uses a solid or liquid material whose atoms are easily excited by radiation
The excited atoms emit visible radiation as they return to their ground state
With a photomultiplier, the photons can be converted into an electrical signal

64. Detectors, 3 Track detectors
Various devices used to view the tracks or paths of charged particles
Photographic emulsion
Simplest track detector
Charged particles ionize the emulsion layer
When the emulsion is developed, the track becomes visible
Cloud chamber
Contains a gas cooled to just below its condensation level
The ions serve as centers for condensation
Particles ionize the gas along their path
Track can be viewed and photographed

65. Detectors, 4 Track detectors, cont Bubble Chamber Wire Chamber
Contains a liquid near its boiling point
Ions produced by incoming particles leave tracks of bubbles
The tracks can be photographed
Wire Chamber
Contains thousands of closely spaced parallel wires
The wires collect electrons created by the passing ionizing particle
A second grid allows the position of the particle to be determined
Can provide electronic readout to a computer