How long does material
remain radioactive? half-life, some uses and implications
What is a radioisotope and what is the half-life of a radioisotope?
Some atomic nuclei are very unstable and only exist for a few
microseconds, seconds, minutes, hours or days before decaying (disintegrating),
these are known as
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 decays to emit alpha, beta, gamma or other nuclear/ionising radiations.
What you can say is the radioactivity must always
over time but never quite reaches zero, except after a very long period of time
The decay follows are particular pattern, illustrated by
the graphs above and below, known as a decay curves.
- The breakdown of these unstable nuclei is called
- Decay is a random event - you can't predict which
isotope nucleus will disintegrate.
- You cannot alter the rate of the decay process - the
radioactive atoms are totally unaffected by the physical or chemical state of
the atoms e.g. in an element or compound and unaffected by change in
temperature or pressure.
- However, despite being a random process, there is a
statistical pattern that the rate of decay follows - known as a radioactive
- The graph of activity follows curve with a gradually
decreasing negative gradient.
- If the gradient is steep, the more unstable is the
radioactivity decay curves
- The 'blue'
radioisotope is more stable than the 'green' radioisotope - gradients less steep.
- The 'green'
radioisotope starts with a greater activity - a more radioactive source, but is
more unstable and disintegrates (decays) much more rapidly.
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).
- 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
It means in one half-life of time, on average, half of the undecayed unstable
nuclei of a particular isotope disintegrate.
- The values of half-lives can vary from a fraction of a
second (highly unstable) to millions of years (relatively much more stable)
See the decay curve graphs 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 e.g. 109 years!
Ideal graph points for a radioisotope's decay curve -
the graph is based on the 'idealised' data table below.
time in half-lives elapsed
Fraction of radioisotope left
Fraction of radioisotope left
Percentage of radioisotope left
- The fraction or % of the radioisotope remaining
is a measure of the activity at any point in time, in fact you can
measure activity in Becquerel (counts/sec, decays/s,
and you might given data in any of the three ways described here - so be
versatile in your thinking!
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,
count rate etc.) is halved,
producing the initially steeply declining curve which then levels out
towards zero after infinite time!
If this data
was obtained in a laboratory experiment, two points should be born in
(i) Before plotting the graph, all measurements
should have the background radiation subtracted from them.
(ii) Your graph is highly unlikely to be a 'perfect'
decay curve. Radioactive disintegration is a random process, so real
data will show small variations from the 'perfect' decay curve - its a
Four Uses of radioactive decay data and half-life
(1) Determination of the half-life of a
Radioisotope and using it to predict future activity
- 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.
Half-life calculation example 1
You would use a Geiger-Marsden counter, or similar
scintillation counter to make measurements of the radioactivity of a
- Radioactivity, or simply 'activity' is measured in
- 1 becquerel = 1 disintegration or decay/second.
- Sometimes the activity might be stated as counts per
second (cps = Bq).
- 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
- 0 min, 400cpm ==> 10 min, 200cpm ==> 20 min, 100 cpm
- In other words, the activity halves every 10 minutes, clearly showing the
half-life is 10
Half-life calculation example 2 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
Half-life calculation example 3 -
prediction of future activity
- Suppose a sample of a radioisotope has an activity of 800
- What will be the activity after three half-lives have
- The rule is that activity halves over every half-life
of time elapsed.
- 800 ÷ 2 = 400, 400 ÷ 2 = 200, 200 ÷ 2 = 100.
- Therefore the final activity is 100 Bq
- You can also express the result as fraction or percent:
- (i) Fraction of activity remaining: 1 ==> 1/2 ==>
1/4 ==> 1/8th (also = 100/8 =
- (ii) Fraction of radioisotope decayed: 1 - 1/8 =
7/8ths (also = 100 x 7/8 =
- Half-life calculation example 4
- calculating half-life from one piece of data
- Suppose the activity of a sample of a
radioisotope has an activity of 8000 Bq (counts/second).
- After 24 hours the activity had dropped to 250
- Calculate the half-life (t½) of
- Now, for every half-life, the activity halves,
therefore we can set out a line of 'halving' logic!
- 8000 ==
t½ ==> 4000
t½ ==> 2000
t½ ==> 1000
t½ ==> 500
t½ ==> 250
- Therefore it took five half-lives to drop from an
activity of 8000 to 250 Bq.
- Therefore the half-life = 24 5 =
Half-life calculation example
- half-life calculation - comparing the activity of two sources after a
period of time
- After the reprocessing of nuclear fuels rods two
fractions of nuclear waste were separated out.
- Radioactive source A had an initial activity of
50 MBq and a half-life of 100 days.
- Source B has an initial activity of 40 MBq and a
half-life of 200 days.
- (a) Which source is the greatest hazard
A is more radioactive than B, 50 MBq > 40 MBq
- (b) Calculate which source is the greatest hazard
after 400 days?
- For source A: 400 days = 400/100 = 4
- Fraction remaining: 1 => 1/2 => 1/4 => 1/8 =>
- So activity of A after 400 days = 50/16 =
3.13 MBq (3 sf)
- For source B: 400 days = 400/200 = 2
- Fraction remaining: 1 => 1/2 => 1/4
- So activity of B after 400 days = 40/4 =
B is more radioactive,
and therefore more hazardous than A after 400 days.
- (c) Sketch a graph to illustrate the given data.
- It should look something like the graph on
- (d) Suggest some implications for the storage of
- For highly radioactive waste materials, with
a short half-life, safe storage for a relatively short time might be
sufficient until it reaches a safe level of activity.
- However, if a less radioactive source has a
much longer half-life, it will remain radioactive for much longer
and need a long-term secure storage facility.
- Radioactive materials with long half-lives
are more of a hazard in the long-run than highly active
radioisotopes with short half lives.
Half-life calculation example 6 - half-life calculation of an isotope used
an industrial process
- When first used, the initial activity of this was
found to be 384 kBq.
- After 24 years the activity was found to be 6 kBq.
- What was the half-life of the radioisotope?
- 384 => 192 => 96 => 48 => 24 => 12 => 6
- From an activity of 384 to 6 takes 6 half-lives.
- So the half-life is 384/6 =
- Example 7.
How long can an radioisotope be useful
- A radioisotope has an initial activity of 6000 Bq,
and a half-life of 10 days.
- In order to be useful, its activity must exceed 700
- For how long, approximately, is the radioisotope
- Working through the half-life decay sequence
- 6000 ==> 3000 ==> 1500 ==> 750 ==> 375
- For 3 half-lives the activity exceeds 700 Bq, so the
useful life is a little over 3 x 10 = 30 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 and more on prediction of radioisotope residues
- 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
- Carbon-14 is formed at a constant rate in the upper
atmosphere by high energy nuclear processes.
- Cosmic rays are very high energy charged particles
the Sun (or even outside of our solar system) that collide with atomic nuclei to release neutrons.
- Nitrogen-14 atoms collide with, and capture neutrons
to form carbon-14 and a proton.
- A neutron smashes out, and replaces, a proton in the
nitrogen-14 nucleus, so carbon-14 is all nicely prepared for the future archaeologist!
- The carbon-14 atoms, like any other carbon atoms,
become part of carbon dioxide in the atmosphere, and carbonates and organic
compounds in aquatic or land-based organisms.
- Carbon-14 is constantly radioactively decaying, but
is also being constantly replaced and balanced by the nuclear reactions in
the upper atmosphere.
- 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
absorbed food from photosynthesis or carbon dioxide given out in respiration
- all parts of the carbon cycle.
- This means the carbon-14 % remains constant as
long as the plant or animal 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)
time in years
% 14C left
Decay curve for carbon-14 disintegration
- 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
(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.
TOP OF PAGE
Atomic structure, radioactivity and
nuclear physics revision notes index
Atomic structure, history, definitions,
examples and explanations including isotopes gcse chemistry
structure and fundamental particle knowledge needed to understand radioactivity gcse physics
is Radioactivity? Why does it happen? Three types of atomic-nuclear-ionising radiation
gcse physics notes
3. Detection of
radioactivity, its measurement
and radiation dose units,
- radioactive materials, background radiation gcse physics revision
4. Alpha, beta & gamma radiation - properties of 3 types of radioactive
nuclear emission & symbols
,dangers of radioactive emissions - health and safety issues and ionising radiation
gcse physics revision
Uses of radioactive isotopes emitting alpha, beta (+/–) or gamma radiation in
industry and medicine gcse notes
6. The half-life of a radioisotope - how
long does material remain radioactive? implications!, uses of decay data and half-life values
archaeological radiocarbon dating, dating ancient rocks
gcse physics revision
actually happens to the nucleus in alpha and beta radioactive decay and why? nuclear
production of radioisotopes - artificial sources of radioactive-isotopes,
cyclotron gcse physics revision notes
fusion reactions and the formation of 'heavy elements' by bombardment techniques
gcse physics notes
9. Nuclear Fission Reactions, nuclear power
as an energy resource gcse physics revision
multiple choice QUIZZES and WORKSHEETS
Tier Radioactivity multiple choice QUIZ
Tier Radioactivity multiple choice QUIZ
Worksheet QUIZ Question 1 on
RADIOACTIVITY - absorption of alpha, beta and gamma radiation
Worksheet QUIZ Question 2 on
RADIOACTIVITY - dangers & monitoring ionising radiation levels
Worksheet QUIZ Question 3 on
RADIOACTIVITY - revision of atomic structure
QUIZ Question 4 on RADIOACTIVITY -
what happens to atoms in radioactive decay?
Worksheet QUIZ Question 5 on
RADIOACTIVITY - uses of radioisotope and half-life data
ANSWERS to the WORD-FILL WORKSHEET QUIZZES
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
TOP OF PAGE
Chemistry Advanced Level Pre-University Chemistry Revision Study Notes for UK IB
KS5 A/AS GCE advanced level physical theoretical chemistry students US K12 grade 11 grade 12
nuclear chemistry radioisotopes and half-lives and calculations
chemistry revision notes: GCSE chemistry, IGCSE chemistry, O level
& ~US grades 8, 9 and 10 school science courses or equivalent for ~14-16 year old
students of radioactivity half-life calculations uses Doc Brown's
school physics revision notes: GCSE physics, IGCSE physics, O level
physics, ~US grades 8, 9 and 10 school science courses or equivalent for ~14-16 year old
students of radioactivity half-life calculations uses
These revision notes on the
half-life of radioisotopes should help with IGCSE/GCSE/ chemistry or physics
courses and A/AS advanced level chemistry or physics courses.
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