How long does material
remain radioactive? half-life, some uses and implications
The half-life of a radioisotope
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
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
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!
Four Uses of decay data and half-life
(1) Determination of the half-life of a
- 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
- 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
- 0s, 400cpm ==> 10min, 200cpm ==> 20min, 100 cpm
- clearly showing the
half-life is 10
- You need to practice these sort of calculations
determination, radioactive residue left, and dating calculations (see below) using the
choice QUIZ (higher GCSE = AS GCE)
(2) Using half-life
data in hazard analysis
or prediction of radioisotope residue
- 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 ==>
- The half-life of a radioisotope has implications about its use and storage and
- 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
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
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)
- 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
For more details
The decay curve for carbon-14 is shown in an Excel file
(4) Geological dating of
- 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%
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.
multiple choice QUIZZES and WORKSHEETS
word-fills on radioactivity
puzzle on radioactivity
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