Edexcel A-level Physics Fission and fusion
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Due to the random nature of radioactive decay, it can never be known which nucleus will decay next. However, half-life gives the time taken for half the nuclei of a sample to decay and thus the activity of the sample to halve. Although half-life is not affected by chemical and physical reactions, different isotopes have different values for half lives, which come with different hazards. Isotopes with shorter half-lives will be more intense due to the fact that more decays will occur per second, which can be extremely dangerous when ingested. Isotopes with longer half-lives will contaminate areas for very long periods of time.
The half-time of an isotope can be calculated using the following formula: t₁/₂ = ln2/λ, where λ is the decay constant of the isotope. By the definition of half-life, the ratio N/N₀ = 1/2, where N = number of nuclei remaining after half-time has elapsed.
The half-life of an isotope can be determined using a graph plotting its activity or the number of nuclei present over time. The half-life will be the point at which the activity or the number of nuclei remaining are half of the initial.
Half-life has numerous applications to every day life. One of these is managing the storage of waste. Since there are great environmental and health concerns associated with radioactivity, radioactive waste must be disposed safely. Half-life helps determine how long the waste must be securely stored for so as not to pose a danger. Another application of half-life is radioactive dating. Radioactive dating determines the age of a radioactive object by comparing the remaining number of nuclei in it to the initial number. A popular example of this is carbon dating. All living things have radioactive carbon-14 in them, which they stop absorbing only when they die. The amount of carbon-14 remaining decreases with time due to radioactive decay. The amount of carbon-14 remaining can be compared to the amount in a living organism to determine its age. This process is more accurate for younger samples, due to the larger numbers of nuclei present.
The number of decaying nuclei in a sample reduces with time due to radioactive decay. This reduction can be expressed as net decline after a certain number of half-lives. Net decline can be expressed as (1/2)ˣ where x is the number of half-lives elapsed.
Fission is the process by which a large atomic nucleus is split up into smaller nuclei. A neutron hits a nucleus and is absorbed by it. This causes the nucleus to become unstable and thus it splits up into smaller nuclei, called the daughter nuclei, and more neutrons. The neutrons released carry most of the energy of the fission reaction as kinetic energy, and thus have to be slowed down before colliding with other nuclei. Fission has an advantage in generating energy over fossil fuels due to the fact that it requires less fissionable material to produce the same amount of energy.
Chain reactions are caused by fission. The additional neutrons produced in a fission reaction collide with other nuclei and cause further fission reactions, which are called chain reactions. Nuclear reactions thus must take place in nuclear reactors to control the speed and temperature of the reactions. The reactor is placed inside a concrete shield so as to protect from the hazardous radioactive nuclei released in the fission reactions. The nuclear fuel, which are the initial nuclei, are held in rods so that the neutrons released in the fission reactions will fly out and cause further ones in other rods. There are also control rods in reactors to control the speed of the chain reactions, which are raised and lowered into it to stop neutrons from travelling between rods. The rods are all in a graphite core, since graphite helps in slowing down the neutrons so that they are absorbed by a nearby fuel rod. The energy released by the fission reactions is used to heat up the coolant and is used to boil water, which in turn will be used to drive turbines and generate electricity.
Nuclear fusion is the process by which small and light nuclei join together to form a bigger and heavier nucleus. Comparing the combined mass of the smaller nuclei to the mass of the resulting nucleus may show that the latter is smaller. This missing mass is converted into energy and is radiated away. Fusion reactions must be quick to occur, so that the repulsion between the two positively charged nuclei does not have time to act. Nuclear fusion must also occur in very high temperatures and pressures to overcome the repulsion between the nuclei.
Induced fission occurs by firing neutrons into a nucleus to cause fission. During this fission process, more neutrons are released from the nucleus. These neutrons in turn hit other nuclei and thus a chain reaction of fission processes is formed. This chain reaction will go on until all the available material has undergone fission. Moderators are used in induced fission. Control rods are also used in induced fission to control the reaction by absorbing neutrons. These rods may be inserted or removed from the reactor whenever necessary. A coolant is used in induced fission to stop the reactor from combusting.
Sketch a graph of the number of nuclei in a radioactive sample against time for 3 half-lives, given that it has a half-life of 35 minutes and that the number of nuclei left after a half-life has elapsed is 4000.
A piece of wood is found to have 0.2 times as many carbon-14 nuclei as a living piece of wood. Given that the half-life of carbon-14 is 5740 years, calculate the age of the piece of wood in years.
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