Probing and Ionising

Scattering

Alpha particle (Rutherford) scattering experiments involved firing charged alpha particles at gold foil. Most of the nuclei went straight through the foil, while a small number were deflected, some at high angles. This showed that the atom is mostly empty space, with most of its mass concentrated in a small, positively charged nucleus. As an alpha particle approaches a nucleus, its kinetic energy is entirely converted to electric potential energy at its point of closest approach.

Electron scattering experiments involve firing electrons at high relativistic speeds. Special relativity is covered in detail in Our Place in the Universe.

Quarks

Protons and neutrons are composed of smaller elementary particles, quarks. A proton is formed by three up, up, and down quarks bound together by the strong force, while a neutron is formed by three down, down, and up quarks. The up quark has a charge of , while the down quark has a charge of . Hadrons are composite particles formed by quarks.

Exchange particles

The fundamental forces are mediated by exchange particles. The gluon is the exchange particle for the strong force.

Nuclear equations

Conservation of mass and conservation of energy individually are not true conservation laws. More generally, mass-energy is conserved, as demonstrated in nuclear reactions. For example, in nuclear fusion, the total mass of the products is lower than the mass of the reactants, with the difference in mass (mass defect) corresponding to the energy released, given by .

In nuclear reactions, charge and lepton number are both conserved. Leptons have a lepton number of +1, while anti-leptons have a lepton number of -1. In beta decay, a neutrino or anti-neutrino is also emitted along with a positron or electron respectively, in order to conserve lepton number. Neutrinos are very light, electrically neutral particles that barely interact with matter.

Quantum model of the atom

A simplified model of the atom can be described by treating electrons as quantum particles in a confined space. Atoms can be thought of as boxes that confine electrons, with the positive nucleus creating a potential energy well that does not allow electrons to escape.

As the electrons are constrained, they form standing waves, which means the electrons must have specific wavelengths for the standing wave (e.g. with one loop, two loops, etc.). This means the electron must only take discrete wavelengths, and by the de Broglie relationship, the electron must only be in discrete energy levels.

Evidence for discrete energy levels

Electrons in atoms occupy discrete energy levels. Evidence for this includes line spectra, where atoms emit or absorb electromagnetic radiation of specific wavelengths, corresponding to specific energy levels. Emission spectra have discrete lines, where each line is carried by photons of a discrete frequency, with energy given by , which corresponds to the difference in energy between two possible energy levels in the atom.

In the Franck-Hertz experiment:

  • A filament is heated, causing electrons to be emitted through thermionic emission.
  • Electrons accelerate towards a wire grid with a positive potential, and pass through.
  • Past the wire grid, there is an anode at a lower potential than the grid, causing electrons to decelerate between the grid and anode.
  • Electrons must have sufficient kinetic energy to reach the anode, where they go through a circuit through an ammeter.
  • The whole setup is performed in a gas at a low pressure.

As the grid potential increases, the current (thus number of electrons reaching the anode) increases initially. Then, at certain p.d.s, the current drops. This is because the electrons have sufficient energy to knock electrons in gas atoms to a higher energy level when colliding, losing energy. These drops happen when the energies of the electrons are a multiple of the gas atom's energy levels, causing inelastic collisions with the gas atoms.

Electron standing waves

Atoms can be considered as a 'box' that traps electrons (due to the potential well near the nucleus). These bound electrons form standing waves, with a de Broglie wavelength that makes an integer number of wavelengths fit within the box.

Ionising radiation

Ionising radiation is radiation that removes electrons from atoms, creating electrically charged ions. There are three types:

  • Alpha particles are strongly ionising. Alpha particles are helium nuclei or . Because they are so massive and so strongly ionising, they rapidly lose energy from successive collisions, causing them to have low penetrating power. Alpha particles have a range of a few centimetres in air.
  • Beta particles are moderately ionising. Beta particles are electrons (beta minus, ), or positrons (beta plus, ). Beta particles have a moderate penetrating power, with a range of around one metre in air, or a few millimetres in metals.
  • Gamma rays are weakly ionising. Gamma rays are high-energy electromagnetic waves, with no mass. This makes them more likely to pass through materials, giving them a strong penetrating power. Gamma rays have a range of hundreds of metres in air, or many tens of centimetres in lead.

Ionising radiation damages living tissue by ionising atoms and breaking molecular bonds, in particular affecting DNA in cells. This can increase the risk of cancer.

Absorption

Denser materials reduce the range of ionising radiation, because they have more atoms to interact with per metre of path, causing radiation to lose energy faster.

Possibly NIS. Intensity of radiation decreases exponentially with the thickness of absorbing material. This can be expressed by the following equation:

Where is the intensity with thickness of material, is the unabsorbed intensity, is the absorption coefficient in , and is the thickness.

The half-thickness is the thickness of material required to reduce the intensity by a half. It is given by

Radiation dose and risk

Absorbed dose is a measure of energy absorbed per unit mass. It is measured in gray .

The effective dose takes into account different types of radiation, and is found by multiplying the absorbed dose by a quality factor. It is measured in Sieverts . The quality factors are:

  • 1 for beta and gamma
  • 20 for alpha.

According to the formula booklet:

Stability and decay

Definitions:

  • Nucleon number: also known as mass number, is the total number of protons and neutrons in each nucleus.
  • Proton number: the number of protons in each nucleus.
  • Isotope: atoms of the same element (same proton number) but with different numbers of neutrons.
  • Atomic mass unit: a standard unit, , used for measuring masses of atoms and subatomic particles, defined as one-twelfth the mass of a carbon-12 atom. A conversion is given in the formula booklet.

Stability of nuclear isotopes depends on the number of protons and neutrons. The strong nuclear force overcomes the electrostatic repulsion between protons, binding protons and neutrons together in the nucleus. The textbook explanation is that extra neutrons provide additional strong force attraction to 'dilute' the repulsion from protons, thus large stable nuclei typically have more neutrons than protons.

Stability of nuclear isotopes mostly depends on energy. If a large amount of energy needs to be put in to pull apart the protons and neutrons of a nucleus, then it must be stable. Thus, the energy of a nucleus must be less than the energy of all the constituent nucleons separately.

Binding energy is a measure of the energy needed to disassemble a nucleus into its individual components. It is given by:

Where is the mass defect, found by subtracting the mass of the nucleus from the total mass of the individual nucleons. If the mass of the atom is given, the mass of the electrons must be subtracted.

Binding energy per nucleon is a measure of how strongly individual nucleons are bound. This gives a good idea of how stable nuclei are.

The plot below shows the general shape of a plot of binding energy against mass number. The lowest point, iron, is the last nucleus that can be achieved through nuclear fusion. On the right, nuclei fall down the slope through nuclear fission.

ABindingenergypernucleon/MeV50100150200246856Fe(moststable)4He235UFusionFission

Nuclear fission

Nuclear fission is the process of splitting heavy nuclei to form lighter nuclei, releasing energy. This is the process used in all commercial nuclear power plants. A chain reaction is where the products of one reaction go on to start one or more new reactions, becoming self-sustaining. In nuclear fission, each fission releases two or more neutrons, which go on to cause more fissions. A moderator can be used to slow neutrons and increase the rate of fissions, while control rods absorb neutrons to decrease the rate of fission.

Many nuclear reactor designs use pressurised water as a moderator and coolant. The water is heated by the energy released in the fission reaction, which then goes through a heat exchanger to create steam, which drives turbines linked to generators, which generate electrical power.

Nuclear fusion

Nuclear fusion is the process of fusing lighter nuclei to form heavier nuclei, releasing energy. This is the reaction that takes place in stars, requiring very high energies (thus temperatures / pressures) to overcome the electric potential barrier.