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.
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
The fundamental forces are mediated by exchange particles. The gluon is the exchange particle for the strong force.
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.
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.
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
In the Franck-Hertz experiment:
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.
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 is radiation that removes electrons from atoms, creating electrically charged ions. There are three types:
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.
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
The half-thickness is the thickness of material required to reduce the intensity by a half. It is given by
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
According to the formula booklet:
Definitions:
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
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.
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 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.