Radioactivity

• Rutherford scattering proved the existence of a nucleus, and disproved the plum pudding model, in which the atom was made of a sphere of positive charge with small areas of negative charge evenly distributed throughout.
• In the Rutherford scattering experiment, most alpha particles pass straight through the foil with no deflection, suggesting that the atom is mostly empty space.
• In the Rutherford scattering experiment, some alpha particles were deflected, suggesting that the centre of the atom is positively charged as the alpha particles were repelled.
• In the Rutherford scattering experiment, a few alpha particles were deflected backwards, suggesting that the centre of the atom was very dense as it could deflect alpha particles, but also very small as only a few were deflected that much.
• Alpha particles are comprised of a helium nucleus, beta particles are comprised of a fast moving electron or positron, and gamma particles are comprised of high energy electromagnetic radiation.
• The range, in air, of alpha radiation is a few centimetres, of beta radiation is a few metres, and of gamma is theoretically infinite.
• Radiation from least to most ionising is gamma then beta then alpha.
• Alpha and beta radiation is deflected by electric and magnetic fields, while gamma is not.
• The penetrating powers of radiation can be used to monitor the thickness of certain materials - eg a beta source can be used for aluminium foil as different thicknesses cause different amount of the source to be detected on the other side and so production can be adjusted.
• Gamma radiation is often used in medicine as it is weakly ionising so does less damage to the body. It is used as a tracer in the body which can be detected, to sterilise surgical equipment as it will kill bacteria and can penetrate though all the equipment, and in radiation therapy to kill cancerous cells.
• Gamma radiation follows the inverse square law as it spreads out in all directions equally, unlike alpha and beta radiation, which is absorbed by matter too quickly.
• Some sources of background radiation are: radon gas released from rocks, nuclear power and weapons, cosmic rays, and rocks containing naturally occurring radioactive isotopes.
• Radioactive decay is a random process, with each given radioactive nucleus having a constant decay probability known as the decay constant, which is the probability of a nucleus decaying per unit time.
• The decay constant can be found as a differential: $\delta$ N/ $\delta$ t = - $\lambda$ N.
• Over long periods of time, radioactive decay can be described as an exponential decay in terms of either the number of undecayed nuclei or the activity of the source in the equations: N = N0 e ^(- $\lambda$ t) or A = A0 e ^(- $\lambda$ t).
• The half life of a source equals ln(2) divided by the decay constant.
• Half life is the time taken for the activity of a source, or the number of undecayed nuclei, to halve.
• The activity of a source is the number of nuclei that decay per second and equals the decay constant multiplied by the number of nuclei in the sample.
• Nuclei with a long half life such as carbon - 14 (about 6000 years), can be used to date organic objects by comparing the current amount of carbon -14 with the initial amount, which is approximately equal in all living things.
• Nuclei with a short half life such as Technetium - 99 m (about 6 hours) are used as radioactive tracers as they last long enough to carry the test out, but short enough to limit exposure.
• Nucleons are held together by the strong nuclear force, however protons also experience a force of repulsion due to the electromagnetic force and so these must be balanced to allow a nuclei to be stable.
• If an nucleus has too many neutrons, it will decay through beta minus emission, where a neutron becomes a proton and an electron and antineutrino are emitted.
• If a nucleus has too many protons, it will decay through beta plus emission or electron capture. In beta plus, a proton becomes a neutron and a positron and electron neutrino are emitted, and in electron capture, an orbiting electron is taken in by the nucleus and combined with a proton, forming a neutron and neutrino.
• If a nucleus has too many nucleons, it will decay by alpha emission to lose two protons and two neutrons.
• If a nucleus has too much energy, it will decay through gamma emission. This usually occurs after another type of decay as the nucleus gets excited.
• The number of neutrons compared to the number of protons needed to keep a nucleus stable does not increase uniformly as the strong force has a limited range while the electromagnetic force is infinite, and so more neutrons are needed to increase the strong force without increasing the electromagnetic and to increase the distance between protons to decrease the magnitude of the electromagnetic force.
• The distance of closest approach of a charged particle to a nucleus is the point at which all the particles kinetic energy is converted to electric potential energy.
• Distance of closest approach can be used to measure the size of a nucleus, however will always be an overestimate as the charged particle will not be able to actually touch the nucleus.
• Electron diffraction can be used to measure nuclear radius by diffracting them through a nucleus and using a graph of intensity against diffraction angle. The equation R = (0.61 $\lambda$ )/ sin $\theta$ can then be used, where R is the radius of the nucleus the electrons were diffracted through, and $\theta$ Is the diffraction angle of the first minimum.
• The radius of an atom can be given by the equation R = R0 A ^1/3, where R0 is a constant and A is nucleon number.
• The density of a nucleus is constant, about 1.5 x10 ^17 kg/m^-3, and much larger than the density of an atom, showing the atom is mostly empty space.
• The mass of a nucleus is always less than the sum of the mass of its constituent nucleons, as this mass difference is converted into energy and released when the nucleons fuse to form a nucleus.
• The binding energy of a nucleus is the energy required to separate the nucleus into its constituent nucleons, and is a potential energy.
• One atomic mass unit is defined as 1/12 th of the mass of a carbon - 12 atom.
• A change of 1 u of mass means that 931.5 MeV of energy is released.
• Nuclear fission is the splitting of a large nucleus into two daughter nuclei. Energy is released as the daughter nuclei have a higher binding energy per nucleon.
• Nuclear fusion is the joining of two smaller nuclei to form one larger nuclei. Energy is released as the larger nucleus has a higher binding energy per nucleon.
• Fusion releases far more energy than fission, and also doesn't release the nuclear waste that fission does, however requires very high temperatures and pressures that currently are not economically feasible on earth.
• The peak of the graph of binding energy per nucleus and nucleon number happens at nucleon number 56: iron, and so iron is the most stable element and nuclei smaller than it can undergo fusion while elements larger than it can undergo fission.
• Fission can be induced by firing a thermal (low energy) neutron into the nucleus of certain elements. The fission reaction then releases neutrons which can collide with other nuclei to cause a chain reaction.