ALL OF PAPER 2

Measuring nuclear radius (closest approach of alpha particles)

Alpha particles are directed towards the atom and are deflected due to electrostatic repulsion. The kinetic energy, E_k, of the alpha particle will reduce and the potential energy, E_p, will increase.

E_k lost = E_p gained

E_k = E_p = Qq/(R x 4πε₀)

R = Qq/(E_k x 4πε₀)

Measuring nuclear radius (electron diffraction)

A beam of electrons is directed at a sample of metal. The electrons diffract around the nuclei in the sample. Intensity of electrons is plotted against angle of diffraction. The angle of the first diffraction minimum (θ_min) is used to determine the diameter of the nucleus and, therefore, the radius

Dependence of nuclear radius on the nucleon number

Use experimental data of samples of different elements to plot R against A^1/3 . The plot will five a straight line through the origin with the gradient equal to R₀. Therefore, it can be said that the nuclear radius of an atom is dependent on the nucleon number of the element

Proving that the density of nuclear material is constant

V = (4πR³)/3 = (4πR₀³A)/ 3

then the density, p

p = m/v = Au/ ((4πR₀³A)/3)

p = u / ((4πR₀³)/3)

All of these are constants!

What does the binding energy per nucleon indicate

Nuclear stability

Induced fision

It can occur by bombarding the uranium isotope ²³⁵₉₂U with neutrons. The uranium isotope is split into 2 smaller nuclei with roughly equal mass and 2 or 3 fission (thermal) neutrons are released. Fission (thermal) neutrons can be harnessed and used to cause more fission events and a chain reaction is induced. Chain reactions only occur if the material used during fission of the uranium isotope is larger than the critical mass. With each fission event, huge amounts of energy are released. Fission chain reactions are used in nuclear reactors in nuclear power plants to create energy that can be harnessed into electricity

Benefits of nuclear power

Huge amounts of power can be generated and less fuel is required than fuels such as fossil fuels for the same amount of energy production

Cons of nuclear power

Can be extremely dangerous and can cause huge harm to the surrounding environment and population

Nuclear radius equation (nucleon number A)

R = R₀A ^1/3

Einstein’s energy equation

E = mc²

Energy changes equation

ΔE = Δmc²

nuclear mass equation

Δm = Zm_p + (A-Z)m_n - m_nucleus

Binding energy

The work required to seperate the nucleus into its constituent parts (i.e. protons and neutrons). The greater it is, the more stable the nucleus

Mass defect

The difference between the mass of the nucleus and the total mass of its individual parts

Einstein’s theory of relativity definition

States that mass and energy are related, and mass can be converted to energy and back. This is what happens in nuclear decay, when the products of a decay have lower mass than the original nuclei - the missing mass is converted to energy

Nuclear fusion

2 low-mass nuclei fuse together to create a larger nucleus. In this process the larger nucleus will, therefore, have a greater binding energy per nucleon than the low mass nuclei

Nuclear fission

A large unstable nucleus breaks apart into 2 smaller, more stable nuclei. The binding energy per nucleon will also increase in this process

Moderator

Controls the speed of the neutrons in the thermal nuclear reactor as the speed needs to be a specific value in order to induce fission. Graphite or water can be used and are chosen for their low probability of absorbing neutrons and low mass

Control rods

Absorbs neutrons in the thermal nuclear reactor to ensure that there is only one thermal neutron per each fission event. They have the ability to absorb even more neutrons if the rate of release of energy needs to be reduced. The material is chosen on their ability to absorb neutrons effectively.

coolant

Extracts the heat in the thermal nuclear reactor and allows it to be transferred to be used to produce electricity. It is usually water or carbon dioxide gas and is used due t the high specific heat capacity of the materials

Shielding in a nuclear reactor

The building housing the reactor is made of concrete walls in order to absorb neutrons and gamma radiation leaving the reactor. The reactor core is also constructed from steel in order to absorb beta radiation as well as some of the gamma radiation and neutrons

Emergency shutdown in a nuclear reactor

The dropping of the control rods directly into the core to entirely cease fission events if the reactor gets too hot

Remote handling in a nuclear reactor

Fuel rods are operated by these devices

Storage in a nuclear reactor

Strict protocols are in place regarding how to store and transport radioactive waste

Einstein’s theory of relativity

mass and energy are related, and mass can be converted to energy and back. This is what happens in nuclear decay, when the products of a decay have lower mass than the original nuclei - the missing mass is converted to energy

Rutherford scattering experiment breakdown

An alpha source provided a beam of alpha particles that were aimed at a thin gold foil. All alpha particles (positively charged) were of the same energy and thre experiment was carried out in an evacuated chamber. The alpha particles were detected by a detector that remained at a fixed radial distance from the point of collision between the particles and the foil. Light was emitted when the particles hit the detector and these emissions of light could be seen by a microscope.

Rutherford scattering experiment results

A small portion of alpha particles were deflected by the foil through angles greater than 90^o. The majority of alpha particles passed through the foil, some with no deflection and some with a small angle of deflection

Rutherford scattering experiment conclusions

The majority of particles passed through the foil, which shows that the atoms making up the foil are likely mostly empty space. Most of the mass of the atom is concentrated in a small nucleus at the centre of the atom. Some alpha particles were deflected, which suggests that the nucleus must be positively charged, as the positively charged alpha particles were repelled as they approached the nucleus.

Alpha consists of

2 protons + 2 neutrons

Beta consists of

electron or positron

Gamma consists of

Photon of energy

Alpha’s range in air

<10 cm

Beta’s range in air

<1 m

Gamma’s range

Obeys inverse square law (1/r²)

Alpha ionisation rate

creates around 10⁴ ions per cm in air

Beta ionisation rate

Creates around 100 ions per mm in air

Gamma ionisation rate

weakly ionising

Alpha absorbed by

thin metal foil or paper

Beta absorbed by

3-5 mm of aluminium

Gamma absorbed by

Several cm of lead

Alpha applications

Measuring thickness of paper, detecting smoke in smoke detectors

Beta applications

Measuring thickness of aluminium foil

Gamma applications

Imaging internal structures of bodies in medicine

Verifying the inverse square law

Use a gamma source and a Geiger Muller tube to measure the intensity of the radiation detected as distance x

Half-life in medicine

To determine which isotope is used to image inside a patient’s body as the source needs to only be radioactive as long as the imaging takes and then should have as little radioactivity as possible. Technicium-99m is an isotope typically used for monitoring blood flow and to image patients using a gamma camera, which images internal structures by detecting gamma radiation emitted from the tracer placed in the body

Nuclear energy levels

When an unstable nucleus undergoes any decay it will emit gamma radiation. The emission of gamma radiation will result in the nucleus losing energy, the nucleus will move from an excited state to its ground state by moving down through its lower energy states

beta + emission process

A positron is emitted from the parent nucelus to leave behind a daughter nucelus. An electron neutrino is emitted as a proton in the nucleys changes into a neutron

beta - emission process

An electron is emitted from a parent nucelus to leave behind a daughter nucelus. An antineutrino is meitted as a neutron in the nucelus changes into a proton

electron capture process

An inner shell electron is captured by a proton-rich nucleus and a proton changes into a neutron. An electron neutrino is also

Decay probability equation

ΔN / Δt = -λN

Number of unstable nuclei equation

N = N₀e^-λt

Half life equation

T_½ = ln 2 / λ

Activity equation (decay constant)

A = λN

Activity equation (initial activity)

A = A₀e^-λ

Inverse square law equation

I = k / x²

Rutherford’s scattering experiment

An ___ in 1908 which provided new evidence about the structure of the atom and resulted in the scientific community moving on from JJ Thomson’s plum pudding model of the atom and this new model

Radioactive decay

occurs when an atom is unstable and emits radiation to obtain a more stable state (it is a random process)

Activity

The number of unstable nuclei that decay per second in a given sample

Half-life (T_1/2)

the amount of time it takes for the activity of the substance to decrease to half its original value

Carbon dating

the examination of the amount of ¹⁴C left in a sample to determine its age as all living organism have a roughly equal ratio to ¹²C to ¹⁴C and when they die, the ¹⁴C slowly decays.

Inverse square law

When the intensity is indirectly proportional to its distance squared

Background radiation

A low level of radiation that is always around on Earth, from both natural and man-made sources of radiation

Natural - nuclear materials in ground, cosmic rays

Man-made - Buildings, nuclear power plants, medical nuclear applications

A nuclear stability graph

A plotting of isotopes by proton number (x-axis) against neutron number (y-axis), classifying them into beta - emitters, alpha emitters, beta + emitters and stable isotopes

Therapeutic ratio

the benefits compared to the potential risks

Investigation of force of a wire

The current is varied, and the change in weight of the magnets is recorded - the change in weight is due to the force of the magnetic field generated by the wire

Alternating current generator

As a wire moves through a magnetic field, the wire cuts magentic field lines, inducing an emf. There is induced emf in a coil that is rotating uniformly with angular rotation in a magnetic field.

Positive FBv

Left hand FBI = FBv

Negative FBv

Left hand FBI = FBv (force in opposite direction)

Charges moving in circular paths

If it occurs in the presence of a magnetic field, we know that the force acting on the particle must be acting towards the centre of the circle. The magnetic field is being used to control the path direction of the moving charge. This concept is used in devices such as cyclotrons used in medical machinery to provide radiotherapy treatment.

Alternating currents

The power deliver to homes and businesses. It’s easier to use root mean square currents and voltages, rather than discussing power supplies as functions.

Transformers

used in the national grid to transmit electricity at high voltages and low current to reduce the power loss in cables

Use of a core in a transfomer

Increase the linkage of magnetic flux between the primary coil and the secondary coil, by providing a path with a high magnetic permeability.

Causes of inefficiency in transformers

Resistance in the cells, eddy currents, work done to produce magnetic field

Efficiency improvements

Lamination reduces energy losses as heat, as the core is constructed from thin sheets of iron separated by an insulating material with high resistivity, which reduces and limits the flow of eddy currents.

magnetic flux and angle relationship in a rotating coil

inverse relationship, inducing an emf

Investigating magnetic fields

A search coil can be used, as the coil moves through a magnetic field, an emf is generated, which can be measured

Force on a current-carrying wire in a magnetic field equation

F = BIL

Force on charged particles moving in a magnetic field

F = BQv

radius of a particle’s circular path equation

r = mv/ BQ

Magnetic flux equation

Φ = BA cosθ

Magnetic flux linkage equation

NΦ

Faraday’s law equation

ε = -N ΔΦ/Δt

emf in an uniformly rotating coil

ε = BAN w sinwt

Root mean square current equation

I_rms = I₀ / √₂

Root mean square potential difference

V_rms = V₀ / √₂

Transformer equation

N_s / N_p = V_s / V_p

efficiency transformers equation

(I_s x V_s) / (I_p x V_p)

Magnetic flux density

force per unit length per unit current on a current-carrying conductor at right-angles to a magnetic field

Fleming’s left hand rule

allows you to determine the direction of motion, field and current in relation to one another

Lenz’s law

the direction of induced current is always such that it is opposed to the change that causes the current

Faraday’s law

the induced emf in a circuit is equal to the rate of change of magnetic flux linkage through the circuit

induced emf

the p.d. induced in a wire due to a moving changing magnetic flux

Cylcotrons

accelerate radioactive particles and control the direction of the particle beams in order to accurately hit the target area on a patient - used in medical machinery to provide radiotherapy treatment

magnetic flux

magnetic field strength through an area

magnetic flux linkage

magnetic field strength through a coil of wire - the flux is multiplied by the number of turns in the coil

Dielectrics properties

High relative permittivity, high capacitance - good electrical insulators

Measuring capacitance

Charge a capacitor fully, measure the potential difference and current (for charge). By calculating the max potential across the capacitor and total charge held, we can find it and the energy stored by the capacitor. Varying the dimensions and dielectric of the capacitor gives the dependence of capacitance on these factors.

Polar molecules

When a capacitor is charged, they rotate to align to the charges on the capacitor. This reduces the electric field in the capacitor, and more charge can be added, increasing the capacitance of the capacitor

Energy relationship with charge and potential difference

All increase across the plates

Charge relationship with time when discharging a capacitor

decreases exponentially - as less and less is stored, the electric field decreases and it is less likely to be forced out of the capacitor