IB PHYSICS Topic : Atomic and Nuclear Physics – Artificial Transmutations

Turning lead into gold was long a dream of alchemists. They never achieved it, but something akin to this occurs every time a nuclear reaction or nuclear decay takes place (%gamma decay excepted): one element becomes another. For example

An atom of carbon becomes an atom of nitrogen.

Radioactive decays are spontaneous processes, and we can do little to change the likelihood of a particular decay happening (chain reactions and atom bombs excepted), but we can promote certain nuclear reactions. For example we can bombard a nucleus with nucleons, %alpha particles or other small nuclei. Such reactions are called artificial transmutations. In general the target nucleus captures the incoming object and an emission of some sort takes place.

The first such artificial transmutation was carried out by Rutherford in 1919. He bombarded nuclei with– particles, producing oxygen. In the reaction protons were emitted.

In fact the label 'artificial transmutations' is a bit misleading, since similar things occur naturally during the post main sequence stages in the lifetimes of stars, producing elements up to iron, and in supernovae, the explosion releasing massive amounts of energy and resulting in the tremendous numbers of particles, which may bombard atoms to produce elements heavier than iron. All of these heavier elements are produced in supernovae.

IB PHYSICS Topic : Atomic and Nuclear Physics – The Geiger Muller Tube

The Geiger – Muller tube can be used to detect ionising radiation and count the number of ionising particles. When gas enters the chamber of either instrument through a window at one end it ionises the molecules of a gas at low pressure. A voltage applied across the tube causes the ions to accelerate towards the anode/cathode and an electrical pulse passes through the circuit. If a steady current is produced this indicates the intensity of radiation.

IB PHYSICS Topic : Atomic and Nuclear Physics – The Pressurised Water Reactor

The pressurised water reactor (PWR) is the design used in most nuclear power stations in the west. These use water as the moderator, to slow down neutrons produced in fission to a speed at which they are likely to induce further fission reactions. This water flows in a pressurised 'primary loop' over the reactor core. The primary loop water circulates and heats water in a secondary loop via a heat exchanger, producing steam which drives the turbine. This system avoid mixing of liquid in the primary and secondary circuits, desirable since the liquid in the primary circuit is highly radioactive.

The PWR can operate at high pressure and temperature, about 160 atmospheres and 315 C, allowing higher efficiencies than other designs. They are safer than many other designs, as an increase in core temperature will cause more of the water in the primary circuit to turn to steam. This will mean neutrons are slowed down less, so remain above the speed at which they are most likely to produce further fission reactions. This negative feedback makes the PWR design very stable, so stable in fact that the design is commonly used in nuclear submarines, and to power steam powered catapults on aircraft carriers.

IB PHYSICS Topic : Atomic and Nuclear Physics – Antimatter

Every form of matter has an equivalent form of antimatter. If matter and antimatter meet, they annihilate each other to produce energy. Antimatter is rare but can be produced in normal radioactive decay processes. For example, a proton decays into a neutron resulting in an anti – electron or positron ()being produced (along with a neutrino):

Anti - particles can form anti – atoms. An anti - electron or positron and an anti - proton could form an anti - hydrogen atom in the same way that an electron and a proton form a normal matter hydrogen atom.

Every antimatter particle has the same mass but the opposite electric charge to it's matter equivalent. Every particle of matter has an antimatter equivalent, opposite in charge but with the same mass as it's particle equivalent. Matter and antimatter can annihilate to produce photons and conversely, a photon can 'decay' to produce matter and antimatter in equal amounts.For this to happen the energy of the photon must be at least equal towhereis the mass of one of the matter – antimatter pair. The difference between the initial photon energy andgoes into the kinetic energy of the particles. The normal rules of conservation of energy and momentum apply during these processes.

In the diagram above left, a gamma ray decays into an electron and it's antiparticle, the positron. The energy of the gamma ray is at leastAny excess of the gamma ray energy over this may go into the kinetic energy of the electron and proton.
In the diagram above right, an electron and it's antiparticle, the positron meet and annihilate. A gamma ray photon is produced. The energy of the gamma ray is at leastAny excess of the gamma ray energy over this is due to kinetic energy of the electron and proton.

IB PHYSICS Topic : Atomic and Nuclear Physics – Nuclear Fission

Nuclear fission is the name given to the process whereby large nuclei break up into smaller ones. In the process energy is released. Fission is the process used in nuclear power stations and many atom bombs. A typical reaction involves bombarding anucleus with neutrons, which may cause the nucleus to fragment. A possible reaction is shown below.

Three more neutrons are produced in this reaction, each of which can cause another fission reaction. A chain reaction is possible, resulting in the production of massive amounts of energy very quickly.

This is what happens in an atom bomb. Onlyof the Uranium isotopes reacts in this way. In nature, only about 0.7% of Uranium is of this isotope, so Uranium is enriched to increase the proportion of The bomb, essentially several uranium fragments, is ignited by bringing these fragments together. This increases the probability of a neutron causing a further decay, so causing a chain reaction.

A similar chain reaction in a nuclear power station is possible but prevented by controlling the rate at which free neutrons can cause further fission reactions with 'control' rods. These absorb stray neutrons.

IB PHYSICS Topic : Atomic and Nuclear Physics – The Implosion Type Atom Bomb

The implosion type atom bomb is a simple design that uses explosives to compress a ball of uranium to a point where the density of neutrons produced by spontaneous decay is enough to cause a chain reaction, hence explode the bomb. The implosion method can use either uranium or plutonium as fuel.

The nuclear fuel is shaped into a sphere – the 'pit' in the diagram, surrounded by conventional explosives. When these are detonated the force of the explosion squeezes the pit into a supercritical mass long enough for uranium to explode. The shock wave that compresses it must be precisely spherical, otherwise the fuel will escape out through a weak point. To create the necessary explosive force in a perfect sphere, shaped explosive charges must be detonated at exactly the same time.

IB PHYSICS Topic : Atomic and Nuclear Physics – Binding Energy Per Nucleon

Whenever a nuclear reaction – fusion or fission releases energy – the products are in a lower energy state than the reactants. The source of this energy is the mass of the reactants, some of which is changed into energy via the equation

If a light nucleus were totally separated into protons and neutrons, then the mass would be greater by a mass(the binding energy) which is equivalent to a mass. Energy needs to be given to the nucleons to enable them to escape the nucleus.

Conversely, if a heavy nucleus is separated into protons and neutrons, then the mass is less by a massEnergy is given out typically when a large nucleus splits into smaller nuclei.

The boundary between light and heavy nuclei in the sense described above is iron. In order to make meaningful comparisons between different nuclei, the binding energy per nucleon is calculated. Then the binding energy per nucleon tends to increase with nucleon number for light nuclei and decrease with nucleon number for heavy nuclei, as in the diagram below. The most stable nucleus is iron.

IB PHYSICS Topic : Atomic and Nuclear Physics – The Random Nature of Radioactive Decay

We cannot tell electrons apart. All electrons have the same mass, the same charge. All electrons in the ground state in the atom of which they are a part all have the same energy, if the atom is the same element. In the same sense, we cannot tell atoms apart. If two atoms are the same element, with the same number of neutrons, both in the ground state, we cannot say which is which.

If an element is radioactive, made up of atoms, all in the same state, then we cannot say at any point which atom will decay in the next time period. All atoms will decay with equal probability. Radioactive decay is a truly random process, not affected by any external conditions – pressure, temperature etc. Although the process of decay is a random process, we can make useful predictions. If we start with a large number of atomswe can expect a certain number to decay in the next time period. Ifwere larger we would expect more decays. On average the rate of decay is proportional to the number of atoms in the sample. We can write

whereis a constant, called the decay constant. The – sign indicates thatis decreasing.

By writingwe can see can see that in a time(whereis infinitesimally small) a fractionof theatoms present will decay on average. This is a prediction. If we have lots of samples, all withatoms initially, sometimes slightly more atoms will decays, sometimes slightly less.

IB PHYSICS Topic : Atomic and Nuclear Physics – Alpha, Beta and Gamma Decay

When a nucleus decays, we can write down an equation that describes the decay. The mass number, and the atomic number must balance in this equation.

Alpha decay

Alpha particles are helium nuclei, writtenDuring alpha decay, a part of the nucleus consisting of two protons and two neutrons is emitted. The remaining fragment will be a different element.
The equation describing the decay is

For example

The mass and atomic numbers balance on both sides of the equation: 241=237 +4 and 95=93+2.
Beta Decay
Beta particles, are fast moving electrons emitted from the nucleus. The electron is emitted when a neutron decays into a proton, resulting also in the emission of a particle called an anti neutrino, labelled

An antineutrino has no charge and probably no mass, (we believe it is massless). The full decay is given by the equation

for example

Gamma Ray Emission
When a gamma ray,is emitted, the element does not change. The gamma ray is emitted because the nucleus is in an excited state. The gamma ray carries away excess energy, leaving behind a more stable nucleus in a lower energy state. The equation describing gamma ray emission is