What was the Rutherford scattering experiment’s conditions?
A narrow beam of alpha particles has fired at a
Thin gold foil target - Multiple layers of gold atoms could stop alpha particles completely, gold is malleable
In a vacuum - Alpha radiation is stopped by air
And the angle of the detector was varied from 0 to 180 degrees.
There was a single energy decay mode since different energies can lead to different angles of deflection.
The source was in a lead container to absorb all alpha particles that wasn’t aimed at the gold foil.
What were the key observations and conclusions of Rutherford’s scattering experiment?
- The majority of alpha particles passed through the foil : atom is mostly empty space
- Some alpha particles were deflected through small angles of less than 10° : positive nucleus at the centre
- Very few alpha particles were deflected straight back at angles greater than 90° : nucleus is extremely small and is where most of the mass and charge of the atom are concentrated
What are the properties of the different types of radiation?
Alpha : 2 protons and 2 neutrons, 2+ charge, 4u mass
Beta minus : Electron, 1- charge, negligible mass
Beta plus: Positron, 1+ charge, negligible mass
Gamma: EM photons, 0 charge, 0 mass
u is defined as 1.66 x 10^-27 kg (1/12 of carbon-12)
What are the different penetrations of different types of radiation?
- Alpha : absorbed by paper or a few centimetres of air
- Beta minus : absorbed by 3mm of aluminium foil paper
- Gamma : absorbed by a large amount of lead or metres of concrete
- Beta plus : typically annihilates with electrons
What are the ionising powers of different types of radiation?
- Alpha : strong ionising power
- Beta minus : weak ionising power
- Gamma : very weak ionising power
What is the inverse square law for gamma radiation?
I = k/x2
where
k is some constant of proportionality in W
x is the distance from the gamma source in m
I is the intensity in W/m2
What are the key precautions taken in the safe handling of radioactive sources?
- Maximise distance between source and person by using tweezers to handle source and keep 2 metres away if observing
- Limit exposure time by removing source from lab when not in use, never pointing source at person and standing behind lead absorber
What are the key sources of background radiation?
- The ground : most rocks contain radioactive materials
- Cosmic radiation : cosmic rays which are high energy particles, radiation emitted when they collide with elements in atmosphere
- Carbon-14 from living plants and animals
How to limit the effect of background radiation on the count rate observed in experiments?
- Take 3 reading of the count rate with a Geiger count rate without the source and mean
- Subtract mean from reading to form corrected count rate
How to eliminate systematic error from background count rate? How to reduce percentage uncertainity?
Systematic:
- Remove all radioactive sources from room and ensure counter and stopwatch are reset before each measurement
Percentage uncertainity:
- Use longer time for source to emit in environment and for count rate to become stable (integration time)
What are the precautions taken when using radiation in a medical context?
- Source must only emit gamma rays (weakly ionising but can escape body and be detected)
- Must have low toxicity
- Half-life must be short enough to not remain in body too long after diagnosis but long enough for diagnosis to take place
What does it mean for radioactive decay to be random and spontaneous?
- Random means you cannot predict when a specific nucleus will decay
- Spontaneous means that decay cannot be influenced by external factors such as temperature
What is activity?
- The number of radioactive decays that occur per unit time measured in Bq (becquerels)
What is the decay constant?
- The probability that a nucleus will decay per unit time
A = λN
where
A is the activity in Bq
N is the number of particles remaining
λ is the decay constant
What are the radioactive decay equations?
N = N0e-λt
where
N is the number of particles remaining
N0 is the initial number of particles
λ is the decay constant
t is the time elapsed in s
similar equations can be formed for activity
A = A0e-λt
What is the equation for half-life?
- Half-life is the average time taken for half of the nuclei in a radioactive source to decay
T1/2 = ln(2) / λ
where
T1/2 is the half-life
λ is the decay constant
What are the key features of the ln(N) against t graph?
The y-intercept is ln(N0).
The gradient is -λ.
