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Nuclear (Energy (Nuclear Power (Waste (U235 only emits alpha radiation and…
Nuclear
Energy
Binding Energy \(E\)
The amount of energy that you would have to supply to a nucleus to break it up into it's constituent, free nucleons
Mass Defect \(\Delta m\)
The amount by which a nucleus' mass is less than the mass of it's constituent, free nucleons
When a nucleus forms, the potential energy of the system of nucleons decreases, and the nucleus becomes more stable - the binding energy is released from the system. This loss in potential energy manifests itself as a loss in mass of the system, and so the nucleus' mass is less than the mass of the constituent nucleons
In order to break apart a nucleus you have to re-resupply the binding energy, to increase the potential energy of the system.
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Nuclear Power
Fuel Rods
Contain subcritical masses of enriched uranium (made of a high percentage of U235), with which control rods can be inserted in between to control the rate of the nuclear reaction
Moderator
Made from graphite or water and slows fission neutrons to thermal neutron speeds in between control rods, through elastic collisions, so that fission neutrons can be used to induce another fission in a chain reaction. Moderator particles should have a mass similar to that of the neutrons to causes the neutrons to loose as much energy as possible (not too much)
Control Rods
Made from Boron and absorb (ideally) all but 1 neutron produced per induced fission. This keeps the reaction going at a steady rate. Control rods can be pushed in further to slow reaction or pulled out to increase rate. Can be entirely released into reactor for emergency shut down
Moderator is heated by energy released in fission. This heat can be used to heat water which turns to steam and so transfers energy away from the reactor. The steam can be used to turn turbines and generate electricity
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Waste
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When first pulled out from the reactor the fuel rods are very hot and so are placed in a cooling pond
Once cool, the fission products can be separated. Useful products can be transported to a medical facility and others can be stored in a shielded container.
The fission products will release energy as they decay, and so should be cooled while they are being stored.
Shielding
Made from thick concrete or lead to shield workers from neutrons and gamma / beta / alpha radiation produced in reactor. Shielding can become radioactive over time by absorbing fission neutrons to create neutron rich nuclei
Maths
Activity \(A\,Bq\)
The number of radiative nuclei decaying per second in a sample
\[A=-\frac{dN}{dt}=\lambda N\]
Decay Constant \(\lambda\,s^{-1}\)
The probability of a particular nucleus decaying per second
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Half life \(T_{\frac{1}{2}}\)
The average time it takes half the number of radioactive nuclei, of a particular isotope, in a sample to decay.
\[T_{\frac{1}{2}}=\frac{\ln{2}}{\lambda}\]
The Random Nature of Radioactive Decay
You can never know which nucleus will decay next, or when a particular nucleus will decay, however there is an equal probability for each nucleus of a particular isotope in a sample to decay per unit time
Decay Modes
Alpha
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Nucleus emits an alpha particle (two protons and two neutrons) and energy.
\[_{Z}^{A}X\rightarrow _{Z-2}^{A-4}Y+_{2}^{2}\alpha+Q\]
Smoke Alarms
A small source of Americium is placed in a small gap in smoke detector. Alpha particles ionise air particles in between two electrodes allowing a small current to flow. Smoke particles in alarm disrupt the flow of electrons, causing current to drop, setting off alarm.
Safe as only a small amount is used and alpha particles will not penetrate through alarm, or far through air
Highly ionising (10,000 air particles per mm moved in air)
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Beta
Plus
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Protons converts to a neutron in the nucleus, via the emission of a positron (beta-plus particle) and an electron neutrino.
\[_{Z}^{A}X\rightarrow _{Z-1}^{A}Y+_{+1}^{0}\beta^{+}+_{0}^{0}\nu_{e}+Q\]
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PET Scanners
Inject a beta-plus emitter into body. Positrons annihilate with electrons in body to produce two gamma ray photons moving in opposite directions. This signal can be used to track the movement of beta-plus source through the body, and track the natural flow of bodily fluids
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Minus
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Neutron converts into proton in the nucleus, via the emission of an electron (beta particle) and an anti-electron neutrino.
\[_{Z}^{A}X\rightarrow _{Z+1}^{A}Y+_{-1}^{0}\beta^{-}+_{0}^{0}\bar{\nu_{e}}+Q\]
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Paper Thickness
Place beta minus source on one side of paper being made, place counter on the other. If paper too thick count rate drops, if too thin count rate increases. Applied in feedback loop.
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Gamma
After a previous decay a nucleus can be left in an excited state. The nucleus de-excites emitting a gamma ray photon of energy equal to the energy lost by the nucleus
After electron capture a nucleus will be left in an unstable state, and so gamma decay usually follows electron capture
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Medical Imaging
Can inject a short half life gamma source into the body to track movement of bodily fluids
Cancer Treatment
Use rotating beam of gamma rays, centred around tumour, to kill cancer cells while limiting the exposure to healthy cells.
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Background Radiation
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Man Made: Nuclear waste, nuclear fallout, nuclear medical facilities etc.
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Eliminate in experiment by taking 3 counts away from any sources and averaging. Subtract from any measurements made.
Structure
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Radius
\[R=R_{0}A^{\frac{1}{3}}\]
Where \(R_{0}\) is the average radius of a nucleon (\(\approx1.4fm\)) and \(A\) is the nucleon number of the nucleus
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Rutherford Method
For an alpha particle incident head-on with a gold nucleus, the initial kinetic energy of the alpha particle must equal the potential energy at the point of closest approach (where the kinetic energy is zero)
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If the initial kinetic energy is known then an upper bound for the distance of closest approach can be found
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Electron Diffraction
Pass a high energy beam of electrons through a thin crystal structure and the electrons in the beam with diffract around the nuclei to produce an interference pattern.
The angle, \(\theta\), of the first minimum in the diffraction pattern is given by:
\[\sin{\theta}=\frac{1.22\lambda}{2R}\]
Where \(R\) is the nuclear radius
This method is much more accurate than Rutherford's method as it does not just give an upper bound and is not affected by the strong nuclear force.
You need to be able to accelerate the electrons to very high velocities for the wavelength of the electrons to be low enough for use.
The consequence of this formula is that all nuclear matter has the same, constant density (assuming the nucleus is spherical)
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