Radioactive decay is random and spontaneous

  1. Random: cannot be predicted; each atom has the same chance of decaying in a given time interval 2. Spontaneous: not affected by external factors like pressure or the presence of other nuclei in the sample 3 types of radioactive decay exist:
Alpha Beta Gamma
Particle Helium nucleus Electron or positron High energy photon
Range in air Few cm  1m 
Absorbed by Thin sheet of paper 1-3mm aluminium Few cm of lead
Deflection in electric field Deflect less Deflect more Undeflected


The reason for the difference in range and absorption is that alpha particles have a large mass and charge, so they interact with surrounding particles and cause strong ionisation. The smaller mass and charge of beta particles make them less ionising. Use a Geiger-Müller tube and a counter to investigate the absorption of different types of radiation by different materials. Remember to account for the background rate. 

Nuclear decay equations can be used to describe different types of nuclear decay.

  1. Alpha: Z → Z−−42 + 42He
  2. Beta-minus: ZZ+1 + 01e + ̅
  3. Beta-plus: ZZ−1 + +01e +

The half-life of an isotope is the time taken for half the active (undecayed) nuclei to decay, or the time taken for the activity of an isotope to half. The activity is the rate at which nuclei decay, measured in becquerels (where one becquerel is one decay per second). The activity depends on the number of undecayed nuclei, so we can write:

A=lambda N

Where lambda  is the decay constant (the probability of decay of an individual nucleus per unit time). The half-life of an isotope can also be calculated using:

lambda tfrac{1}{2}=ln(2)

You can measure the half-life of an isotope such as protactinium-234 using a GM-tube. A sealed plastic bottle containing an organic solvent and a solution of uranyl(VI) nitrate in water is used to separate protactinium, the daughter isotope, from thorium (protactinium is soluble in the organic solvent but thorium isn’t). First determine the background count rate. Shake the plastic bottle to dissolve protactinium in the organic layer. Then measure the time taken for the count rate from the protactinium to halve. The window of the GM tube can’t touch the bottle, as this risks contamination. 

The number of undecayed nuclei and activity of radioisotopes decrease exponentially. They can be described by these equations:

N=N_{o}e^{-lambda tfrac{1}{2}}

A=A_{o}e^{-lambda tfrac{1}{2}}

Radioactive decay can be simulated using dice: if you remove dice showing a certain number after each roll. The number of remaining dice demonstrates a constant ratio property over time, so behaves exponentially. It can also be described using iterative modelling:

  1. Start with a given number 0 of undecayed nuclei in the sample
  2. Select a small interval of time, ∆. This must be small compared to the half-life so you can assume the activity does not change significantly.

Calculate the number of nuclei decaying using 

frac{Delta }{Delta t}N=lambda N therefore Delta N=(lambda Delta t)times N

  1. Calculate the new number of nuclei by subtracting the number decaying from the original number
  2. Repeat for further short intervals of time.

Radioactive dating can be used to find the age of substances, e.g. carbon dating.

  1. High-speed protons in cosmic rays collide with atoms in the upper atmosphere, producing neutrons
  2. These in turn collide with nitrogen-14 nuclei to form carbon-14 nuclei
  3. Carbon-14 nuclei undergo beta decay with a half-life of 5700 years. So the amount of N-14 in the atmosphere is replenished.
  4. Comparing the amount of C-14 in a sample to the amount of C-14 in the atmosphere allows you to work out the time elapsed since death (when living, the amount of C-14 stays constant due to photosynthesis, ingestion, respiration etc.)

C-14 dating has limitations: burning of fossil duels and volcanic eruptions increases the amount of C-12 in the atmosphere, changing the ratio of C-14 to C-12. Also, beyond a few half-lives the amount of remaining C-14 in the sample becomes so small that activities are comparable to the background count rate. 

To date rocks, you cannot use C-14 as its half-life is too short. Beta-minus decay of rubidium-87 can be used instead.