Nuclear Physics

Rutherford Scattering
-demonstrated existence of nucleus

Thomson’s plum pudding model - sphere of positive charge with small areas of negative charge evenly distributed throughout.
Rutherford scattering lead to nuclear model of atom.

Rutherford’s apparatus includes an alpha source and gold foil in an evacuated chamber which was covered in a fluorescent coating - can see where alpha particles hit inside of the chamber. Microscope which was moved around the outside of the chamber to observe the path of the alpha particles.

• Most alpha particles passed straight through the foil with no deflection - suggests atom is mostly empty space

• A small amount of particles were deflected by a large angle - suggests centre of the atom is positively charged, as positively charged alpha particles were repelled from the centre and deflected

• Very few particles were deflected back by more than 90^o - suggests the centre of the atom is very dense as it could deflect fast moving alpha particles but also that is was very small as a very small amount of particles were deflected by this amount

The above results conclude that the atom has a small, dense, positively charged nucleus at its centre.

α, β and γ radiation

Radiation - unstable nucleus emits energy is the form of EM waves / subatomic particles to become more stable. Types of radiation consist of alpha (a), beta (β) and gamma (γ).

Alpha (a)
range: 2 - 10cm
ionising: highly
deflected by electric and magnetic fields?: yes
absorbed by?: paper

Beta (β)
range: around 1m
ionising: weakly
deflected by electric and magnetic fields?: yes
absorbed by?: aluminium foil (3mm)

Gamma (γ)
range: infinite range
ionising: very weakly
deflected by electric and magnetic fields?: no
absorbed by?: several metres of concrete / several inches of lead

Due to their differing penetrating powers, these type of radiation emitted from a source can be identified using this experiment:

1. Using a Geiger-muller (GM) tube and counter, find the background count when the source is not present.
2. Place the source of radiation close to the GM tube and measure the count rate.
3. Place a sheet of paper between the source and GM tube and measure count rate again, if the count rate decreases significantly, then the source is emitting alpha radiation.
4. Repeat the above step using aluminium foil and several inches of lead. If there is a significant decrease in count rate for aluminium foil, then beta radiation is being emitted and if there is a significant decrease in count rate for the lead block, then gamma radiation is being emitted.

Gamma radiation - very weakly ionising so does less damage to our bodies than alpha and beta particles, therefore it’s used in medicine:

• as a detector - radioactive source with short half life (reduces exposure), emitting gamma radiation. Source can be injected into patient and gamma radiation can be detected using gamma cameras in order to help diagnose patients.

• to sterilise surgical equipment - as gamma radiation kills bacteria present on equipment

• in radiation therapy - gamma radiation can be used to kill cancerous cells in a targeted region of the body (i.e. tumour) but will also kill any healthy cells in the region.

Precautions for medical staff & patients: reduced exposure times, use of shielding.

As gamma radiation travels in air, it spreads out in all directions equally, therefore the intensity of gamma radiation follows an inverse square law:

I = k/x<sup>2

I = intensity of radiation
k = constant
x = distance from source</sup>

You can investigate this relationship using a simple experiment where you measure the count rate of a gamma source at different distances from the GM tube, making sure to adjust for the background radiation. Then you can plot a graph of corrected count against 1 / x², which will form a straight line verifying the equation above.

Alpha radiation is highly ionising, and therefore can be incredibly dangerous if inhaled or ingested as it can ionise body tissue. Beta particles are less ionising but can still cause damage to body tissue, and prolonged exposure to gamma radiation can cause mutations and damage to cells.

Due to radiation’s dangerous, radioactive sources must be handled safely by:

• using long handled tongs to move the source

• storing the source in a lead-lined container when not in use

• keeping the source as far away as possible from yourself and others

• never pointing the source towards others

Background radiation is constant so when taking count rate readings, measure the BG radiation first, then subtract this value to find the corrected count, which is the actual count rate caused by the source.
Corrected count = Total count rate - background count

Examples of sources of background radiation:
→ Radon gas - released from rocks
→ Artificial sources - caused by nuclear weapons testing and nuclear meltdowns
→ Cosmic rays - enter the Earth’s atmosphere from space
→ Rocks containing naturally occurring radioactive isotopes

Radioactive decay
random process - cannot predict when next decay will occur
the constant decay probability of a radioactive nucleus is known as the decay constant (λ) - the probability of a nucleus decaying per unit time
ΔN / Δt = -λN

N = N₀e^-λt

N = no. of nuclei, N₀ = initial no. of nuclei, λ = decay constant, t = time passed

Radioactive decay is exponential, the time taken from the number of nuclei to halve will be constant - HALF LIFE (T_1/2)
this can be calculated graphically, by plotting a graph of the no. of nuclei against time and measuring the time taken for the sample size to halve.
More accurate method - plot graph of ln (N₀) against time, forming straight line graph, the modulus of the gradient of the line is the decay constant, which can be used to find half-life.

T_½ = ln2 / λ

The activity of a radioactive sample is the no. of nuclei that decay per second - proportional to the no. of nuclei in the sample, where the decay constant is the constant of proportionality:

A= λN

As activity is directly proportional to the no. of nuclei it follows the sample exponential decay equation:

A = A₀e^-λt

They’re proportional - the time taken for activity to halve is equal to the half-life - and activity of a sample is much easier to measure than the no. of nuclei so activity is often used to find the half-life of a sample.

The decay constant can be used to model the decay of a nuclei only when there is is a large no. of nuclei in a sample

half life of radioactive nucleus affects the way it can be used:

• Dating of objects - nuclei with a long half-life such as carbon-14, which has a half-life of 5730 years can be used to date organic objects (i.e. found is archaeological sites). This can be used my measuring the current amount of carbon-14 and comparing it to the initial amount, the percentage of which is approximately equal in all living things.

• Medical diagnosis - nuclei with relatively short half-lives are used as radioactive tracers in medical diagnosis. i.e. Technetium-99m is ideal for use in medical diagnosis as it’s a pure gamma emitter, it has a half life of 6 hours, which is short enough to limit exposure but long enough for tests to be carried out, and it can be easily prepared on site.

Activity and half life of radioactive nuclei also affects the way they must be stored:
Extremely Long half life - (i.e. steel casks underground) to prevent nuclei from damaging environment and the people that may be living around them hundreds of years into future.

Nuclear Instability

Nuclei are held together by strong nuclear force, however protons experience force of repulsion due to the electromagnetic force and so forces are out of balance. This causes nuclei to become unstable and will experience radioactive decay. 4 reasons why a nucleus is unstable and depending on why, it will decay in a different way:

1. Too many neutrons - decays through beta-minus emission (sometimes neutron emission), one of the neutrons in the nucleus changes into a proton and a beta-minus particle and antineutrino is released. The nucleon number is constant, while the proton number increased by 1.

2. Too many protons - decays through beta-plus emission / electron capture. In beta plus, a protons changes into a neutron and a beta-plus particle and neutrino is released. In electron capture, an orbiting electron is taken in by the nucleus and combined with a proton causing the formation of a neutron and neutrino. In both types of decay the nucleon number stays constant, whilst proton number decreases by 1.

3. Too many nucleons - decays through alpha emission, the nucleon number decreases by 4 and proton number decreases by 2.

4. Too much energy - decays through gamma emission, usually occurs after different type of decay, like alpha/beta as nucleons become excited and have excess energy

Nuclear radius

estimate the nuclear radius by calculating the distance of closest approach of a charged particle. For example, an alpha particle fired at a gold nucleus will have an initial KE which can be measured, as it moves towards the positively charged nucleus it will experience an electrostatic force of repulsion and slow down as its kinetic energy is converted to electric potential energy. The point at which the particle stops and has no kinetic energy is its distance of closet approach, its electrical PE is equal to its initial KE due to conservation of energy. Calculate distance using equation of electric potential:
V = 1/4πε₀ Q/r

As electric potential is the potential energy per unit charge of a positive charge. If we multiply this by the charge of our particle = equation for the electric PE

E_elec = 1/4πε_{0 X} Q₁Q₂/r

ε₀ = permittivity of free space
Q₁Q₂ = charge of the nucleus/charged particle
r = the distance to the centre of the nucleus/distance of closest approach

Electron diffraction is another method for calculating nuclear radius.
Electrons are leptons - won’t interact with nucleons in the nucleus through the SNF like alpha particles, so electron diffraction gives a far more accurate estimate of nuclear radius.

The electrons are accelerated to very high speeds so that their De Broglie wavelength is around 10^-15 m, and are directed a very thin film a material in front of a screen causing them to diffract through the gaps between nuclei and form a diffraction pattern.

The diffraction pattern formed is a set of concentric circles with a central bright spot, that gets dimmer as you move away from the centre, using this pattern you can plot a graph of intensity against diffraction angle from which you can find the diffraction angle of the first minimum.

sinθ = 0.61λ / R
θ = diffraction angle of the first minimum, λ = De Broglie wavelength of the electrons, R = radius of nucleus that the electrons were scattered by.