• Some atomic nuclei are very unstable and only exist for a few seconds or minutes. Others are very stable and take millions of years to decay away to form another atom. A measure of the stability of a radioisotope is given by its half-life.
• The half-life of a radioisotope is the average time it takes for half of the remaining radioactive atoms to decay to a different atom.
• It means in one half-life of time, on average, half of the undecayed unstable nuclei of a particular isotope disintegrate.
• See the decay curve graph below.
• It can vary from a fraction of a second to millions of years!
• The radioactivity of any sample will decrease with time as the unstable atoms decay to more stable atoms, though sometimes by complex decay series routes e.g. ₉₂U isotopes eventually decay to ₈₂Pb isotopes.

For Higher students only. The older a sample of a radioactive material, the less radioactive it is. The decrease in radioactivity follows a characteristic pattern shown in the graph or decay curve. After every half-life, (in this case 5 days, working out from the graph), the % radioisotope (or radioactivity) is halved, producing the initially steeply declining curve which then levels out towards zero at infinite time!

6b. Four Uses of decay data and half-life values

---

(1) Determination of the half-life of a Radioisotope

• The radioactivity from a radioisotope is measured over a period of time.
  • Graphical or mathematical analysis is performed to calculate the time it takes for the radioactivity of the isotope to halve.
  • For short-lived radioactive isotopes, the radioactivity is likely to be measured in terms of the count rate.
  • Therefore the half-life will be the time it takes for the count rate to halve.
• An example of what this means is shown in the diagram below.
  • 
  • The graph shows the rapid decay of a very unstable radioactive isotope in terms of count rate per minute (cpm) versus minutes.
  • From the graph you can work out the time (half-life) it takes for half of the radioactive atoms to decay from the decrease in count rate.
  • e.g. in terms of time elapsed, count rate ==> we get
  • 0s, 400cpm ==> 10min, 200cpm ==> 20min, 100 cpm etc.
  • clearly showing the half-life is 10 minutes.
• You need to practice these sort of calculations of half-life determination, radioactive residue left, and dating calculations (see below) using the multiple choice QUIZ (higher GCSE = AS GCE)

• From the half-life you can calculate how much of the radio-active atoms are left e.g. after one half-life, ¹/₂ is left, after two half-lives, ¹/₄ is left, after three half-lives, ¹/₈ is left in other words its a 'halving pattern' etc.
  • Example Q: The half-life of a radioisotope is 10 hours. Starting with 2.5g, how much is left after 30 hours?
    • 2.5g =10h=> 1.25g =10h=> 0.625g =10h=> 0.3125g (after total time of 30h)
    • Another way to think - if the time elapsed is equal to a whole number of half-lives you can just divide the 30 h by 10 h, giving 3 half-lives.
    • Therefore you just have to halve the amount three times!
      • e.g. 2.5 ==> 1.25 ==> 0.625 ==>  0.3125g
• The half-life of a radioisotope has implications about its use and storage and disposal.
  • If the half-life is known then the radioactivity of a source can be predicted in the future (see (1) above).
  • Plutonium-244 produced in the nuclear power industry has a half-life of 40 000 years!
  • Even after 80 000 years there is still a 1/4 of the dangerously radioactive material left.
  • Quite simply, the storage of high level nuclear reactor radioactive waste is going to be quite a costly problem for many (thousands?) of years!
  • Storage of waste containing these harmful substances must be stable for hundreds of thousands of years! So we have quite a storage problem for the 'geological time' future! see also dangers and background radiation.
• Radioisotopes used as tracers must have short half-lives, particularly those used in medicine to avoid the patient being dangerously over exposed to the harmful radiation, but a long enough half-life to enable accurate measurement and monitoring of the tracer.

(3) Archaeological dating with the isotope carbon-14

* Most carbon atoms are of the stable isotope carbon-12. A very small % of them are radioactive due to carbon-14 with a half-life of 5700 years. It decays by beta emission to stable nitrogen-14. Archaeologists can use any material containing carbon of 'organic living' origin to determine its age. This can be bone, wood, leather etc. and the technique is sometimes called radiocarbon-14 dating.

• When the 'carbon containing' material is in a living organism there is a constant interchange of carbon with the environment as food or carbon dioxide. This means the carbon-14 % remains constant. When the organism is dead the exchange stops and the carbon-14 content of the material begins to fall as it radioactively decays.
• Compared to when it was 'alive' ...
  • if an object has ¹/₂ (¹/₂ of 1, 50%) of the expected carbon-14 it must be 5700 years old,
  • if it only has ¹/₄ (¹/₂ of a ¹/₂, 25%) of the expected ¹⁴C left, the object it must be 11400 years old (5 700 + 5 700),
  • and if only ¹/₈ (¹/₂ of ¹/₄, 12.5%) of the ¹⁴C left it is 17100 years old (11 400 + 5700) etc. etc.
  • 
  • Example of a simple dating calculation.
  • An archaeologist had a sample of bone from a prehistoric skeleton analysed for its carbon-14 content.
  • The bone sample was found to contain 6.25% of the original carbon-14, calculate the age of the skeleton.
  • Just using a simple halving calculation technique you get ...
    • 100% ==> 50% ==> 25% ==> 12.5% ==> 6.25%
    • So to get to 6.25% takes four half-lives
    • therefore the age of the skeleton is 4 x 5700 =  22800 years
• For more details The decay curve for carbon-14 is shown in an Excel file webpage

• Certain elements with very long half-lives can be used to date the geological age of igneous rocks and even the age of the Earth. has a half-life of 1.3 x 10⁹ years. It decays to form .
• If the argon gas is trapped in the rock, the ratio of potassium-40 to argon-40 decreases over time and the ratio can be used to date the age of rock formation i.e. from the time the argon gas first became trapped in the rock. The method is more reliable for igneous rocks, rather than sedimentary rocks because the argon will tend to diffuse out of porous sedimentary rocks but would be well trapped in harder and denser igneous rocks.
  • If the ⁴⁰Ar/⁴⁰K ratio is 1.0 (50% of ⁴⁰K decayed, 50% left )  the rocks are 1.3 x 10⁹ years old
  • If the ⁴⁰Ar/⁴⁰K ratio is 3.0 (75% of ⁴⁰K decayed, 25% left)  the rocks are 2.6 x 10⁹ years old
  • If the ⁴⁰Ar/⁴⁰K ratio is 7.0 (87.5% of ⁴⁰K decayed, 12.5% left)  the rocks are 3.9 x 10⁹ years old
    • These are worked out on the basis of 100% =half-life=> 50% =half-life=> 25% =half-life=> 12.5% etc. etc.
• Long lived isotopes of uranium (element 92) decay via a complicated series of relatively short-lived radioisotopes to produce stable isotopes of lead (element 82). The uranium isotope/lead isotope ratio decreases with time and so the ratio can be used to calculate the age of igneous  rocks containing uranium compounds.

or Harder-Higher Radioactivity Quiz

  five word-fills on radioactivity * Q2 * Q3 * Q4 * Q5and ANSWERS!

crossword puzzle on radioactivity and ANSWERS!

Revision KS4 Science GCSE/IGCSE/O level Chemistry Information Study Notes for revising for AQA GCSE Science, Edexcel 360Science/IGCSE Chemistry & OCR 21stC Science, OCR Gateway Science  WJEC gcse science chemistry CCEA/CEA gcse science chemistry O Level Chemistry (revise courses equal to US grade 8, grade 9 grade 10) A level Revision notes for GCE Advanced Subsidiary Level AS Advanced Level A2 IB Revise AQA GCE Chemistry OCR GCE Chemistry Edexcel GCE Chemistry Salters Chemistry CIE Chemistry, WJEC GCE AS A2 Chemistry, CCEA/CEA GCE AS A2 Chemistry revising courses for pre-university students (equal to US grade 11 and grade 12 and AP Honours/honors level courses)