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!

## Rutherford Scattering

**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 9×109 (or 8.85×109 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 = 8.85×10^-9

## Electron Scattering

**Target**– Nucleus**Projectile**– Electron (at high energy)**Conclusion**– Scattering electrons can be used to determine the size of the nucleus.

*What evidence is there that the nucleus contains more than one type of particle?*

*What is an isotope, include an example*

*Why do different isotopes of the same element have the same chemical properties?*### Electron Scattering Measures the Nucleus

*Why can’t alpha particles be used to probe inside a nucleus?*

*What can be used instead and why?*

*Sketch a diagram to show what path an electron scattered by the nucleus might take.*

*Why do electrons scattering off a nucleus create a diffraction pattern?*

*What can this diffraction pattern tell us?**Why do electrons need to be accelerated to such high energies for this to work?*

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

*always*three quarks. Mesons are always two quarks consisting of a quark/anti-quark pairing. A U (up quark) = 2/3 e charge. A D (down quark) is work -1/3 e charge. There are anti-quarks too which have the opposite charges. U = up quark.

- 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 / 2mλ²

If we substitute in λ = 2d/n (which came from d = nλ/2…

KE = n²h² / 2m(2d)²

En = n²E

However, this is only an approximation.

## Evidence for the Size of a Hydrogen Atom

We 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 = – ke**² / **r. It is negative as one of the charged is positive and the other is negative.

### Conclusion

En = -13.6eV/n²

### Small Summary

To 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 Radioactivity

### Nuclear Fission – What is it?

### Why does Nucleus Fission happen?

### Nuclear Fusion – What is it?

## Comparing Nuclear Radiation

**Beta 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.

**Alpha Radiation**

- 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.

**Gamma Radiation**

- 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

*What is meant by ‘stable’?**Why does N = Z for small stable nuclei but N > Z for large ones?*

At N = Z, the strong interaction force of a nucleus is greater than the electrostatic force between protons. As the proton number increases, the electrostatic force repelling the protons from each other will increase. Therefore, more neutrons are needed to decrease the electromagnetic force (by increasing the gap between the protons).

*What is special about Z = 82?**and*protons, it emits alpha particles (helium nucleus which consists of two protons and neutrons).

## Design of a Pressurized Water Reactor

*What is the role of the moderator?*

*What is the role of the control rods?*## Shielding

**Half thickness –**Thickness needed to reduce the number of photons to half.

I = I(0) / 2

## Radiation Dose

**Absorbed Dose = Energy deposited per kilogram**(measured in grays)

**Dose Equivalent = Absorbed Dose x Quality Factor**(measured in Sievert)

- 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**.

**Example **

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 = 2000×10^-6 x 0.05 = 0.0001% (it is very small).

2) Multiply by the number of people – what does this tell you?

**438,200 people**.

### How Do Smoke Detectors Work?

## Eddy Currents

**opposing the direction of the original flux lines**. Therefore, the change in flux in the core will reduce causing the EMF in the secondary coil to decrease. Eddy currents are a resistance to the transformer.

## Transformers

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/dt

The 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/dt

But, 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

perpendicularto 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.

### Motor Design

- 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.

#### Problems

- 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.

## Electromagnetic Equations

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.

### Example

- Φ = BA
- B = Φ / A
- A = 0.7 x 1.2 = 0.84m²
- B = 1700×10^-3 / 0.84 = 2.02T

- Φ = ΛNI
- 27 = 3.2 x 1500 x Λ
- Λ = 27/4800
- Λ = 5.6×10^-3 WbA^-1turn^-1

### Flux Linkage

Flux Linkage (Φ) = Flux (Φ) x Number of turns (N)

#### Faraday’s Law

EMF = -N x dΦ/dt

#### Lenz’s Law

The 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

## Faraday’s Law

## 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 velocity

At the speeds near to the speed of light, the total energy of a particles changes too:

Total Energy =γmc²

This makes clear that to work out **γ**, it is:

γ = Total Energy / Rest energy

Where the rest energy can be worked out from E = mc² and the total energy = Rest Energy + Kinetic Energy.

## The Electric Field

An 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.

#### Quick Calculation

- E = F/Q
- F = E x Q
- F = 10 x 1.6×10^-19 =
**1.6×10^-18 N** - F = ma
- a = F/m
- a = 1.6×10^-18 / 9.1×10^-31 =
**1.8×10^12 m/s****²**

## The Linear Accelerator

## Particle Physics

*What quantities must be conserved according to the law of physics?*

*What is the is the significance of the conservation of momentum in particle-antiparticle annihilation?*#### Bubble and Cloud Chambers

*How are tracks made in a bubble chamber?*

*How are tracks made in a cloud chamber?*

*What is the significance of the direction of curvature of the track?*

*What is the significance of the radius of curvature of the track?*

*What type of particles do not make any tracks and why?*#### Fermions and Bosons

*What is a fermion? Give examples.*

*What is a boson? Give examples.*

*How do they behave differently?*- 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.

#### The Neutrino

*What is a neutrino?*

*Where do neutrinos come from?**How was the neutrino discovered?*

- 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

### The Forces

**Gravity**

- Boson – Graviton.
- Source – Mass.
- Relative Strength – 10^-39.
- Range – Infinite.

**Weak Interaction**

- Boson – W+, W- and Z.
- Source – Weak Charge.
- Relative Strength – 10^-5.
- Range – 10^-18 m.

**Electromagnetism**

- Boson – Photon.
- Source – Charge.
- Relative Strength – 10^-2.
- Range – Infinite.

**Strong Interaction**

- Boson – Gluons.
- Source – Colour.
- Relative Strength – 1.
- Range – 10^-15 m.

## Electromagnetic Field Equations and Graphs

*always*

**positive to negative**. When you are drawing field lines, think of what direction a positive charge would move if placed in the field. This is the direction of the field lines. Notice in the below diagram that the equipotential lines distance increases the further away from the charge. This makes clear that the field density decreases the further away from the charge.

E = kQ / r²

**The area under this graph is the electric potential.**

V = kQ / r

**The gradient of this graph represents the electric field strength at distance r.**

F = kQq / r²

**The area under this graph is the potential energy of the particle with charge q at a distance of r from Q.**

PE = kQq / r

**The gradient of this graph is the force on particle with charge q from being distance r from particle with charge Q.**

Great website really helps!!!

Whoah, this is really well done! Thank you very much kind stranger

Great job!

Mistake needs correcting:

Towards the end of the page under electromagnetic equations is

“Permeance (Λ) = ( Permittivity (µ) x Area (m²) ) / Length (L)”

The symbol mu is correct but the word should be ‘permeability’ not permittivity (the latter relates to electric rather than magnetic fields. Worth correcting otherwise excellent article.

Thank you for spotting that out for me!