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
microseconds, seconds, minutes, hours or days.
Others are very stable and take millions of years to decay away to form another atom.
Some isotopes are completely stable and do not undergo
radioactive decay at all.
The radioactivity (emissions) of any radioactive material
always decreases with time.
A measure of the stability of a radioisotope is given by its half-life
Unstable nuclei disintegrate at random, you cannot
predict which one decay to emit alpha, beta, gamma or other nuclear/ionising radiations.
What you can say is the radioactivity must always decay
over time but never quite reaches zero, except after a very long period of time
The decay follows are particular pattern, illustrated by
the graph below, known as a decay curve.
The half-life of a radioisotope is the
average time it takes for half of the remaining undecayed radioactive nuclei
(atoms) to decay to a different nucleus (atom).
It means in one half-life of time, on average, half of the undecayed unstable
nuclei of a particular isotope disintegrate.
- The graph will drop steeply for very unstable nuclei but
show a very small gradient if more stable.
- Every graph shows the same mathematical feature which is
that for a particular time interval the amount of
See the decay curve graph below
representing the behaviour of relatively unstable radioactive-isotope with a
half-life of 5 days.
- Within a half-life, half of the remaining
unstable nuclei decay (disintegrate), equivalent to a 50% reduction in
- A short half-life means the activity
(radioactivity) will fall quickly e.g. falls by 50% in a few minutes
with lots of unstable nuclei decaying.
- so, a short half-life means relatively rapid
decay, a long half-life means a relatively slow decay and measurable
radioactivity lasts much longer.
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
- This means from radioactivity measurements we can analyse
the data and calculate from the graph the half-life of a radioactive-isotope or
some calculation based on an initial level of activity and a later measurement
of the decreased activity. Whatever method, you need accurate activity data
linked to time.
- This also means that we can make predictions of activity
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
The y axis can represent the %
radioisotope left OR the measured radioactivity.
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 after 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.
You would use a Geiger-Marsden counter, or similar
scintillation counter to make measurements of the radioactivity of a
- The graph shows the rapid decay of a very
unstable radioactive isotope in terms of count rate per minute (cpm) versus
- Although not shown, before plotting the graph, you should
do a blank test for the background radiation and subtract this
from ALL the readings.
- You would do a blank test by taking several readings
without the presence of the radioisotope and use the average to correct the
- An alternative to this is to use heavy lead shielding to
protect the Geiger counter from background radiation, but should still do a
blank test with the identical experiment setup.
- 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
- 0min, 400cpm ==> 10min, 200cpm ==> 20min, 100 cpm
- clearly showing the
half-life is 10
- 2nd example not using a graph, but 'simple fraction'
- Suppose a sample of a radioisotope gives an initial
activity of 1200 counts per minute (cpm).
- If the activity has fallen to 150 cpm after 180 days,
calculate the half-life of the radio-isotope.
- The simple method just involves involving halving from
the initial value of activity until you reach the final value.
- In terms of activity: 1200 == ÷2 ==> 600 == ÷2 ==> 300 ==
÷2 ==> 150
- so, to get from 1200 to 150 required 3 halvings.
- From the definition of half-life, this means 3 half-lives
elapsed for the activity to drop from 1200 cpm to 150 cpm.
- Therefore the half-life is 180÷3
= 60 days
- 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)
- You can do a class experiment to illustrate the random
nature of radioactive decay and half-life e.g.
- Use say 50 normal dice numbered 1-6 shaken in a
- Make zero time that before the first 'throw' (tip the lot
out of the box), so t = 0, d = 50
- Throw the dice and remove all sixes, pretending they were
the ones to disintegrate (decay).
- Make this t = 1, d = dice left.
- Just repeat a few times, removing all the sixes each time
and counting the dice left.
- After, say six goes, plot the number of dice left versus
the time interval 0, 1, 2, 3 etc. and a decay curve graph will emerge.
- You can then estimate the 'half-life' in time intervals.
- The time interval could represents, seconds, minutes,
hours ... millions of years, it doesn't matter!
(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
For more details
The decay curve for carbon-14 is shown in an Excel file
- 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 as
long as the organism is alive!
- 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
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
(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.
RADIOACTIVITY and NUCLEAR PHYSICS INDEX
Atomic structure, fundamental particles and radioactivity
is radioactivity? Why does it happen? What radiations are emitted?
3. Detection of radioactivity, measurement,
dose units, ionising radiation sources, background radiation
properties and dangers of alpha, beta & gamma radioactive emission
uses of radioactive Isotopes emitting alpha, beta or gamma radiation
6. Half–life of radioisotopes, how
long does material remain radioactive? Uses of decay data & half–life values
changes in radioactive decay? how to write nuclear
equations? Production of Radioisotopes
Nuclear fusion reactions and the formation of 'heavy elements'
9. Nuclear Fission Reactions, nuclear power energy resources
multiple choice QUIZZES and WORKSHEETS
word-fills on radioactivity
puzzle on radioactivity
OTHER CHEMICAL CALCULATION PAGES
What is relative atomic mass?,
relative isotopic mass and calculating relative atomic mass
formula/molecular mass of a compound or element molecule
Law of Conservation of Mass and simple reacting mass calculations
Composition by percentage mass of elements
in a compound
Empirical formula and formula mass of a compound from reacting masses
(easy start, not using moles)
Reacting mass ratio calculations of reactants and products
moles) and brief mention of actual percent % yield and theoretical yield,
and formula mass determination
Introducing moles: The connection between moles, mass and formula mass - the basis of reacting mole ratio calculations
(relating reacting masses and formula
moles to calculate empirical formula and deduce molecular formula of a compound/molecule
(starting with reacting masses or % composition)
Moles and the molar volume of a gas, Avogadro's Law
Reacting gas volume
ratios, Avogadro's Law
and Gay-Lussac's Law (ratio of gaseous
Molarity, volumes and solution
concentrations (and diagrams of apparatus)
do volumetric titration calculations e.g. acid-alkali titrations
(and diagrams of apparatus)
Electrolysis products calculations (negative cathode and positive anode products)
e.g. % purity, % percentage & theoretical yield, volumetric titration
apparatus, dilution of solutions
(and diagrams of apparatus), water of crystallisation, quantity of reactants
required, atom economy
Energy transfers in physical/chemical changes,
Gas calculations involving PVT relationships,
Boyle's and Charles Laws
Radioactivity & half-life calculations including