Week 7 - Electron & Photon Interactions with Matter

Explain Coulomb’s Law

Electrostatic force between 2 charges is directly proportional to the product of the magnitude of the 2 charges and inversely proportional to the square of the distance between the charges.

Explain how an object becomes charged

By the movement of electrons:

• Losing electrons = positively charged

• Gaining electrons = negatively charged

State the formula for calculating force between 2 charges.

F = k_e x (q₁ x q₂) /d²

Where:

• F = force

• k_e = Coulomb’s constant

• q₁ = magnitude of force 1

• q₂ = magnitude of force 2

• d = distance between 2 forces

State the unit of charge and relation to an electron

Coulomb (C)

e = 1.6 × 10^-19C

Explain voltage/EMF

Voltage or Electro-Motive Force (EMF) is the amount of work/force required to push electrons through a circuit.

State the units of voltage

Volts (V) in which 1V = 1J/C

Explain electron voltage

The amount of energy gained by an electron that accelerates through a potential difference of 1V.

Explain current and give units

The flow of charge per unit time, measured in Ampere (A) in which 1A = 1C/s

Explain resistance and give units

Forces within a conductor that opposes current, measured in Ohms in which 1 Ohm is 1V/A.

Describe Ohm’s Law and state the relevant formula

In ohmic materials, resistance remains constant regardless of the applied voltage or current.

V = I x R

Where:

• V = voltage

• I = current

• R = resistance

Explain power and state the formula and units

Energy per unit time, measured in Watts (W)

P = V x I

P = (charge x voltage)/time

How do companies measure energy?

The amount of energy supplied over a certain time period, measured kilowatt-hour (kWh).

kWh = power x time

Name and explain the 2 types of current and what each is typically used for

• Direct Current (DC) - flow of charge in one direction only, used in medical radiations

• Alternating Current (AC) - flow of charge alternates directions, used in larger appliances

Name the 2 theories for metallic bonding

• Electron sea model

• Band theory

Explain the electron sea model

A metal arranged as an array of positive ions surrounded by a sea of delocalised valence electrons.

Explain band theory

Solids containing differing energy bands of electrons, including a completely filled valence band of valence electrons as well as a conduction band of freely moving excited electrons that have crossed the forbidden energy gap between the 2 bands.

Explain the difference between resistivity and resistance.

Resistance is the opposition of current within a material based on its length and cross-sectional area which can be altered, whereas resistivity is the opposition of current within a material based on its inherent properties which cannot be altered.

State the formula of resistance

R = (ρ x L)/A

Where:

• R = resistance

• ρ = resistivity/constant of proportionality

• L = length

• A = cross-sectional area

Show the relationship between diameter and cross-sectional area

A = π x (d/2)²

d = √4A/π

Explain how temperature affects resistance and resistivity and state the relative formula

Increasing temperature increases kinetic energy and vibration of conductor material atoms, therefore resulting in difficulties in electrons carrying current to pass through through conductor.

R(T) = R_o[1+a(T-T_o)]

Where,

R(T) = resistance at time T

R_o = initial resistance

T_o = initial time

a = coefficient of resistivity

Explain the coefficient of resistivity

a or the coefficient of resistivity is a value representing a materials inherent resistivity in which a positive coefficient applies to conductors and superconductors while a negative coefficient applies to semiconductors only.

Explain the difference between conductors and insulators using band theory.

Conductors are solid metals with high conductivity and minimal resistance due to having no forbidden energy gap in which valence electrons cannot freely move into the conduction band. Whereas insulators are non-metals with low conductivity and high resistance due to their large forbidden energy gap of 10eV in which their conduction band is empty.

Explain superconductors

Materials that have zero resistance below a certain temperature, known as critical temperature,

Explain semiconductors

Metalloids that are partially conducting material with a small forbidden energy gap of 1eV.

Describe 2 ways conductivity of semiconductors can be increased

• Increasing temperature increases kinetic energy of electrons which increases conductivity

• Doping the metalloid with another element darastically increases conductivity

Name and describe the 2 types of semiconductors

• Intrinsic - pure metalloids

• Extrinsic - metalloid doped with another element

Name and describe the 2 types of extrinsic semiconductors

• N-type - contains a negative current which is governed by electron flow

• P-type - contains a positive current which is governed by positive holes

Explain how N-type semiconductors work with the example of silicon doped with phosphorus

The doping of a metalloid adds an additional energy band known as the donor state which is below the conduction band. Eg. When silicon is doped with phosphorus, the additional phosphorus electron that cannot make a covalent bond with silicon is in the donor state energy band and can easily be excited into the conduction band, carrying current.

Explain how P-type semiconductors work with the example of silicon doped with boron

The doping of a metalloid adds an additional energy band known as the acceptor state which is above the valence band. Eg. When silicon is doped with boron, only 3 covalent bonds are made in which there is a missing electron, creating a positive ‘hole’. When a voltage is applied, a silicon valence electron is excited into the acceptor state, attracted to this positive ‘hole’ and attempting to fill its electron absence, leaving another ‘positive hole’ behind. These positive ‘holes’ are what govern the flow of electrons, therefore creating a positive current.

Describe a rectifier

A p-n junction dioxide which is the junction of p and n-type semiconductors which converts AC to DC.

Explain the difference between x-ray and gamma photons

Both have the same energy, frequency and wavelength, their only difference is that x-rays originate from electron-electron interactions and gamma rays originate from nuclear decay.

Name the 5 major photon interactions and state if they are absorption or scattering processes

• Elastic/Rayleigh Scattering - scattering only

• Photoelectric Effect - absorption only

• Compton Effect - both

• Pair Production - absorption only

• Photodisintigration - absorption only

Explain elastic scattering

When an incident photon with energy less than electron binding energy collides with an electron but does not transfer energy, only changes direction. Therefore incident and scattered photon have the same energy, wavelength and frequency.

Explain photoelectric effect

When an incident photon with energy greater than electron binding energy collides with an inner shell electron and transfers all of its energy, overcoming electron binding energy and ejecting the now photoelectron from the atom. Electrons in outer shells move to fill in this vacancy, releasing characteristic x-rays with energies based on the difference in shell binding energies.

Explain how the probability of photoelectric effect is affected by incident photon energy and Z value of the irradiated material

• The probability of photoelectric effect occurring is inversely proportional to the cube of the incident photon energy

• The probability of photoelectric effect occurring is directly proportional to the cube of the Z value of the irradiated material

Explain Compton effect

When an incident photon with energy much greater than the electron binding energy collides with a valence electron which overcomes small binding energy and is ejected from the atom. The photon has only transferred a small amount of energy and scatters in a new direction with slightly decreased frequency and increased wavelength.

Describe the angle of deflection of a Compton/scattered photon

The angle of deflection is the angle between the direction of travel of the incident vs scattered photon, indicating the amount of energy lost to the valence electron/electron binding energy. A greater angle of deflection corresponds with greater energy loss/binding energy,

Apply the law of conservation energy to the compton effect

Incident photon energy is equal to electron binding energy, plus Compton electron energy, plus scattered photon energy.

Explain how the probability of the Compton effect is affected by incident photon energy and Z value of the irradiated material

• The probability of the Compton effect is inversely proportional to incident photon energy

• The probability of the Compton effect is independent of Z value as the interaction occurs with a valence electron

Explain pair production

When an incident photon with energy greater than 1.02 MeV interacts with the nucleus of an atom, transferring all of its energy into mass, producing an electron and positron pair. This pair of particles annhilate each other, creating 2 photons of 511keV energy each which travel 180 degrees from one another.

Explain photodisintegration

When an incident photon with energy greater than 10 MeV interacts with the nucleus of an atom, transferring all of its energy and immediately ejecting a nucleon/nuclear fragment.

Explain how the probability of pair production and photodisintigration are affected by incident photon energy and Z value of the irradiated material

• The probability of these interactions are directly proptional to incident photon energy with a threshold of at least 1.02 MeV for pair production and 10 MeV for photodisintegration

• The probability of these interactions are directly proportional to the Z value of the irradiated material

Give the definitions of attenuation, absorption and scatter

• Attenuation - the reduction in radiation beam intensity/energy

• Absorption - the energy transfer to the irradiated material from the radiation beam

• Scatter - the movement of radiation in a direction that differs from the primary radiation beam

Explain the relationship between attenuation, absorption and scatter

Attenuation is the loss of energy from the processes of absorption and scatter when interacting with an irradiated material.

Name and describe the 3 factors affecting attenuation

• Irradiated material thickness - increasing thickness increases the number of particles and therefore absorption and attenuation

• Irradiated material density - increasing density increases the number of particles and therefore absorption and attenuation

• Incident photon energy/ wavelength - increasing energy will decrease interaction with matter and therefore attenuation

State the radiation beam intensity equation

I_x = I_o x e^-μx

Where:

• I_x = intensity at thickness x

• I_o = initial intensity

• μ = attenuation coefficient

Explain differential attenuation

The amount of attenuation differing within different parts of the same structure, creating an intensity profile which is used to produce an image

Explain half value layer (HVL)

The thickness of an attenuating material that reduces radiation beam intensity by 50%.

Describe attenuation coefficients and name the 2 types

Inherent property that indicates a materials effectiveness of attenuation. 2 types include:

• Linear attenuation coefficient (LAC)

• Mass attenuation coefficient (MAC)

Explain LAC

The fraction of attenuated photons per unit thickness of an irradiated material, dependent on density and can therefore be different for the same material depending on temperature.

State the formula for LAC

LAC = ln(2)/HVL

Explain MAC

The fraction of attenuated photons per unit cross section per unit mass of irradiated material, dependent on density and is therefore the same for all forms of the same material.

Give the formula for MAC in relation to LAC

MAC = LAC/density