In this article, I will cover every topic from G495 including the (in chronological order) Rutherford Scattering, electron and deep inelastic scattering, quark combinations, energy levels of electrons, evidence for the size of a hydrogen atom, nuclear radioactivity (fission and fusion), alpha, beta and gamma radiation, curve of stability analysis, design of a pressurized water reactor, shielding and half thickness, radiation dose, how risk is calculated, eddy currents, transformers: how they work and design of them, the catapult field, motor design, electromagnetic equations, flux linkage, Faraday's and Lenz' laws, moving charged particles and relativity, the electric field, the linear accelerator, particle physics, particle identification, the forces, and, finally, electromagnetic field equations with graphs. Please feel free to skip to the parts most relevant to you - I do not expect you to read it all in one go!
- Target - atom (Gold)
- Particle fired in - alpha particle (also known as the nucleus of a helium atom)
- Conclusion -Mass and charge are concentrated in a tiny nucleus and that atoms are mainly made up of empty space.
Distance of Closest Approach
- F (force between two charged particles) = kQq / r2. k is a constant which is around 9x109 (or 8.85x109 for more accuracy).
- E (electric field strength when the charge is at a point) = kq / r2 . The charge 'q' is whatever charge is causing the electric field you are entering.
- V (electric potential) = kq / r.
- PE (electrical potential energy) = kQq / r.
d (distance at closest approach) = Ze^2 / (2πE x KE)
Where k = 1/4πE = 8.85x10^-9
- Target - Nucleus
- Projectile - Electron (at high energy)
- Conclusion - Scattering electrons can be used to determine the size of the nucleus.
Electron Scattering Measures the Nucleus
So that the wavelength is about the same dimensions as of a nucleus.
- Rutherford scattering which is an exponential graph.
- Diffraction curve.
Deep Inelastic Scattering
- Target - Proton (quarks inside proton/neutron)
- Projectile - Electron (at high energy).
- Conclusion - there is the existence of three particles inside a proton and neutron being quarks.
Combinations of Quarks
- A proton is made up of UUD = +1.
- An anti-proton is made from anti-quarks of UUD = -1.
- A neutron is made from UDD = 0.
- An anti-neutron is made from anti-quarks of UDD = 0.
Energy Levels of Electrons
KE = h² / 2mλ²If we substitute in λ = 2d/n (which came from d = nλ/2...
KE = n²h² / 2m(2d)²
En = n²EHowever, this is only an approximation.
Evidence for the Size of a Hydrogen AtomWe know that the potential energy of a charged particle is kQq/r when the charged particles are distance 'r' apart from each other.
For a hydrogen atom, it has one proton and one electron. Therefore, PE = - ke² / r. It is negative as one of the charged is positive and the other is negative.
En = -13.6eV/n²
Small SummaryTo find evidence for:
- An atom containing a tiny nucleus, we can use Rutherford's scattering which fires alpha particles at an atom and notes the deflection caused by the positively charged nucleus. Only a few out of thousands of fire alpha particles are deflected 180 degrees making clear the nucleus is extremely small.
- The atoms in the nucleus are positively charged, we can fire a positively charged alpha particle which will be repelled by the nucleus proving that it is positive (or fire an electron at it which will become attracted to it).
- Radius of the nucleus, we can use an electron scattering which creates a graph combining the Rutherford scattering and direction curve. The 'first dip' is the size of the nucleus and is of the order of 10^-15m.
- Protons and neutrons contain smaller particles called quarks, we can use deep inelastic scattering which fired electrons at high energies at protons and neutrons.
Nuclear Fission - What is it?
Why does Nucleus Fission happen?
Nuclear Fusion - What is it?
Comparing Nuclear Radiation
- Structure - Beta + is a positron / Beta - is an electron.
- Charge - Beta + has a charge of +e / Beta - has a charge of -e.
- Penetrating power - Medium: it is stopped by 3mm of aluminium or 10-20cm of air.
- Ionizing power (how easily does it lose or gain an electron) - Medium.
- Deflected by electric and magnetic fields? - Yes, out of all the radiation, it has the highest charge:mass ratio.
- Structure - two protons and two neutrons (nucleus of a helium).
- Charge - +2e.
- Penetrating power - Low: it is stopped by 1cm of air or skin or a sheet of paper.
- Ionizing power (how easily does it lose or gain an electron) - High because it has a large charge.
- Deflected by electric and magnetic fields? - Yes, second most because the charge to mass ratio of alpha particle is less than that of a beta.
- Structure - high energy and frequency gamma ray.
- Charge - No charge.
- Penetrating power - High: need lead to stop it (but it can never completely stop it but reduce it exponentially.
- Ionizing power (how easily does it lose or gain an electron) - Low because it cannot attract atoms with charges.
- Deflected by electric and magnetic fields? - No as the gamma ray has no charge.
The Curve of Stability
Design of a Pressurized Water Reactor
What is the role of the moderator?
I = I(0) / 2
- Gamma radiation has a factor of 20.
- Beta radiation, gamma and X-ray have a factor of 1.
- Neutron radiation has a factor of 10.
How is Risk Calculated?The risk of something happening (e.g. cancer) is often expressed as a percentage per Sievert per person per year.
There are 62.6 million people in the UK and the average level of background radiation is 2000uSv per year. The risk of cancer from this is 5% per Sievert per person per year. Calculate how many people are likely to get cancer from background radiation over a 70 year lifespan.
We can break this question down into three steps:
1) Calculate the percentage risk for a 2000uSv dose - what does this tell you?
Percentage risk from 2000uSv = 2000x10^-6 x 0.05 = 0.0001% (it is very small).
2) Multiply by the number of people - what does this tell you?
How Do Smoke Detectors Work?
N (secondary) / N (primary) = V (secondary) / V (primary)The ratio of the number of turns on the secondary coil to that on the primary coil is the same as the ratio of the voltage on the secondary coil to that on the primary.
How Does a Transformer Work?
EMF = - N x dΦ/dtThe above equation is Lenz's law. The negative sign means that the EMF induced always opposed the field that is causing it.
Transformer Design of the Core
The Catapult Field
What Factors Affect the Power of a Motor?
P = dW/dtBut, W = F x d (where d is the distance moved in the same direction of the force).
Mom (turning effect: torque) = F x d (where d is the distance moved perpendicular to the direction of the force).W = F x d indicated that greater power goes into the motor if the coil (rotor) is turning faster. But, a fast turning coil has large eddy currents so these oppose the motion of the coil so it reaches an upper limit where torque is zero. This is because all the energy is going into moving the rotor. At lower speeds, the rotor will produce a more useful power output.
- Using an electromagnet for the stater as well as a coil for the motor.
- Good magnetic circuit. This requires the use of materials of relatively high permeability and few and small air gaps (so the magnetic circuit has a high permeance).
- Use more than one pair of poles (N+S) to make torque smoother and more consistent. If there is more than one poles, a multi-part commutator is needed.
- There will be sparking at the commutator/brushes. The brushes are made from carbon which are a good conductor. Metals produce an oxide layer which is not a good conductor. When carbon oxides, it turns to carbon dioxide. Therefore, the oxidation turns some of the carbon atoms to gas maintain the conductance of the carbon brushes.
- Noise and vibrations which could lead to resonance.
Flux density (B) = Flux (Φ) / Area (A)This can be re-arranged as:
Flux (Φ) = Flux density (B) x Area (A)Flux is measured in Weber (Wb), Area in m² and flux density in Wbm^-2. 1 Tesla = 1 Wbm^-2. Another equation for the flux is:
Flux (Φ) = Permeance (Λ) x Number of turns in a coil (N) x Current (I)The equation for Permeance is:
Permeance (Λ) = ( Permeability (µ) x Area (m²) ) / Length (L)The units for permeance is WbA^-1turn^-1. An increase in the current increases the field around the wire/conductor. Increasing the number of turns of the coil adds the field lines from each turn of the wire to produce a larger field. The definition of permeance is how much flux that can pass through the magnetizable medium. It is like the conductance for electrical flow but for magnetism.
- Φ = BA
- B = Φ / A
- A = 0.7 x 1.2 = 0.84m²
- B = 1700x10^-3 / 0.84 = 2.02T
- Φ = ΛNI
- 27 = 3.2 x 1500 x Λ
- Λ = 27/4800
- Λ = 5.6x10^-3 WbA^-1turn^-1
Flux Linkage (Φ) = Flux (Φ) x Number of turns (N)
EMF = -N x dΦ/dt
Lenz's LawThe induced EMF opposes the change of flux causing it (hence the minus sign). It is often useful to link the flux density and flux linkage equations to get the following:
Flux Linkage Φ = NAB
Moving Charged Particles and Relativity
and its initial position - Classical physics (Newton's law)
Kinetic Energy = 1/2 x mass x velocity squared.
momentum = γ x mass x velocityAt the speeds near to the speed of light, the total energy of a particles changes too:
Total Energy = γmc²This makes clear that to work out γ, it is:
γ = Total Energy / Rest energyWhere the rest energy can be worked out from E = mc² and the total energy = Rest Energy + Kinetic Energy.
The Electric FieldAn electric field is a type of force field (not in the sci-fi sense!). Consequently, it exerts a force on an object with property that the field influences. For electric fields, this property is charge.
For a uniform electric field, E = F / Q = V / D. Electrical field strength can be measured in V/m or N/C. For a uniform field, the value of E is constant.
- E = F/Q
- F = E x Q
- F = 10 x 1.6x10^-19 = 1.6x10^-18 N
- F = ma
- a = F/m
- a = 1.6x10^-18 / 9.1x10^-31 = 1.8x10^12 m/s²
The Linear Accelerator
Bubble and Cloud Chambers
Fermions and Bosons
- Bosons want and like to be together (which is a reason why we have lasers).
- Fermions don't like to be together and prefer to be split up from each other.
- During experimentation with beta + and - decay, scientists found that the conservationist equations were unbalanced.
- Therefore, to make the equations balanced and conserved, another particle must have been created.
- This particle's properties, to balance the equation, must have 0 mass, 0 charge, and a lepton number of 1.
Particle Identification Diagram
- Boson - Graviton.
- Source - Mass.
- Relative Strength - 10^-39.
- Range - Infinite.
- Boson - W+, W- and Z.
- Source - Weak Charge.
- Relative Strength - 10^-5.
- Range - 10^-18 m.
- Boson - Photon.
- Source - Charge.
- Relative Strength - 10^-2.
- Range - Infinite.
- Boson - Gluons.
- Source - Colour.
- Relative Strength - 1.
- Range - 10^-15 m.
Electromagnetic Field Equations and Graphs
E = kQ / r²
V = kQ / r
F = kQq / r²
PE = kQq / r