Chapter 29 Nuclear Physics

Rutherford showed the radiation had three types Alpha (He nucleus) Beta (electrons) Gamma (high-energy photons)

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

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

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:

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

Mass It is convenient to use unified mass units, u, to express masses 1 u = x kg Mass can also be expressed in MeV/c 2 1 u = MeV/c 2

Summary of Masses Masses ParticlekguMeV/c 2 Proton x Neutron x Electron9.109 x x

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

Nuclear Stability, cont Light nuclei are most stable if N = Z (P=N) Heavy nuclei are most stable when N > Z (N>P) 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 (N>83)

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

Binding Energy per Nucleon

Binding Energy Notes Except for light nuclei, the binding energy is about 8 MeV per nucleon

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

Radioactivity – Types Three types of radiation can be emitted Alpha particles The particles are 4 He 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

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

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 The decay rate or activity, R, of a sample is defined as the number of decays per second (dps)

Decay Curve The decay curve follows the equation N = N o 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

Units The unit of activity, R, is the Curie, Ci 1 Ci = 3.7 x decays/second (dps) The most commonly used units of activity are the mCi and the µCi

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

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

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

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

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

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

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 Very weak interaction with matter

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

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

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

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

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

Nuclear Reactions – Example Alpha particle colliding with nitrogen: Balancing the equation allows for the identification of X So the reaction is

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

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

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

Units of Radiation Exposure Roentgen [R] That amount of ionizing radiation that will produce 2.08 x 10 9 ion pairs in 1 cm 3 of air under standard conditions That amount of radiation that deposits 8.76 x J of energy into 1 kg of air Rad (Radiation Absorbed Dose) That amount of radiation that deposits J of energy into 1 kg of absorbing material

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

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