Basic Nuclear Physics

1
Basic 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
• 1938 Hahn and Strassman discovered nuclear
  fission
• 1942 Fermi and collaborators achieved the first
  controlled nuclear fission reactor

5
Ernest Rutherford

• 1871 1937
• Discovery of atoms being broken apart
• Studied radioactivity
• Nobel prize in 1908

6
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

7
Symbolism

• Symbol
• 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

8
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

9
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 1.602 177 33 x 10-19 C

10
Mass

• It is convenient to use unified mass units, u, to
  express masses
• 1 u 1.660 559 x 10-27 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 931.494 MeV/c2

11
Summary of Masses
12
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

13
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 10-14 m
• For silver, he found d 2 x 10-14 m
• Such small lengths are often expressed in
  femtometers where 1 fm 10-15 m
• Also called a fermi

14
Size of Nucleus, Current

• Since the time of Rutherford, many other
  experiments have concluded
• Most nuclei are approximately spherical
• Average radius is
• ro 1.2 x 10-15 m

15
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

16
Nuclear Models

• Liquid-Drop Model treat the nucleons like liquid
  molecules. Good on estimating the nuclear binding
  energy but not on the finer nuclear structures
  such as the stability rules and angular momentum.
• Independent Particle Model (shell model) treat
  nucleons just like atomic electrons. This model
  can explain many nuclear properties such as the
  magic number etc.

17
The Independent Particle Model
18
Maria Goeppert-Mayer

• 1906 1972
• Best known for her development of shell model of
  the nucleus
• Shared Nobel Prize in 1963

19
Partial Nuclear Energy Diagram of 131Xe
20
Nuclear Spin and Spin Magnetic Moment

• Proton or neutron has intrinsic spin 1/2
• Nuclear orbital angular momentum ?I(I1) (I
  integer or half-integer, nuclear spin quantum
  number)
• Nuclear magneton ?n(eh)/(4?mp)5.05x10-27 J/T in
  analogous to electron ?B 9.274 x 10-24 J/T
• Magnetic momentum of a free proton is 2.7928 ?n
  and a free neutron -1.9135 ?n

21
Nuclear Spin Angular Momentum
22
Principles of Magnetic Resonance Imaging
23
Principles of MRI
24
Principles of MRI
25
Principles of MRI
26
Nuclear Forces
27
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

28
Nuclear Stability, cont

• Light nuclei are most stable if N Z
• Heavy nuclei are most stable when N gt 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 gt 83

29
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

30
Binding Energy per Nucleon
31
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 gt 40
• This suggests that the nuclear force saturates
• A particular nucleon can interact with only a
  limited number of other nucleons

32
Marie Curie

• 1867 1934
• Discovered new radioactive elements
• Shared Nobel Prize in physics in 1903
• Nobel Prize in Chemistry in 1911

33
Radioactivity

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

34
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

35
Distinguishing Types of Radiation

• A radioactive beam is directed into a region with
  a magnetic field
• The gamma particles carry no charge and they are
  not deflected
• The alpha particles are deflected upward
• The beta particles are deflected downward
• A positron would be deflected upward

36
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

37
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
• ?N -? N ?t
• ? 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

38
Decay Curve

• The decay curve follows the equation
• N No e- ?t
• 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

39
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

40
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

41
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

42
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

43
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

44
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

45
Beta Decay Electron Energy

• The energy released in the decay process should
  almost all go to kinetic energy of the electron
  (KEmax)
• Experiments showed that few electrons had this
  amount of kinetic energy

46
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

47
The Neutrino ?
48
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

49
Pure ?- (Negatron) Emission
50
Beta (Negatron) Emission
51
Positron ? Emission
52
Fate of the Positron
53
Positron Emission Tomography (PET)
54
Electron Capture
55
Electron Capture
56
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 photons are called gamma rays, very high
  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

57
Gamma Decay

• Nuclear transition from an excited state to a
  lower energy state
• Nuclear excited state can be created by particle
  collision or as a result of nuclear decay.

58
Gamma Decay
59
Metastable States and Isometric Transition
60
Internal Conversion
61
Auger Electrons or X-ray
62
(No Transcript)
63
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 doesnt change either A or Z

64
Enrico Fermi

• 1901 1954
• Produced transuranic elements
• Other contributions
• Theory of beta decay
• Free-electron theory of metals
• Worlds first fission reactor (1942)
• Nobel Prize in 1938

65
Uses of Radioactivity

• Carbon Dating
• 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

66
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

67
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
• See table 29.2

68
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

69
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

70
Nuclear Reactions Example

• Alpha particle colliding with nitrogen
• Balancing the equation allows for the
  identification of X
• So the reaction is

71
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

72
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

73
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

74
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

75
Units of Radiation Exposure

• Roentgen R
• 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 kg of air
• Rad (Radiation Absorbed Dose)
• That amount of radiation that deposits 10-2 J of
  energy into 1 kg of absorbing material

76
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 dose in rad X RBE

77
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

78
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 to reduce the chances
  of infection

79
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

80
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

81
Detectors, 2

• Semiconductor Diode Detector
• 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

82
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

83
Detectors, 4

• Track detectors, cont
• Bubble 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