Initially, students may regard atoms as the fundamental chemical particles. True, electrons can be chipped off an atom, and possibly all an atom’s electrons stripped off to leave a bare nucleus; yet according to the simple story, the nucleus is still fixed and determines the element by its charge, Ze.

Therefore, to change one element into another, the alchemist’s dream of lead into gold, would require a change of nuclear charge. At first sight this seems impossible because the nucleus is buried deep in the atom bound together by tremendous forces. But it does happen in radioactive elements.

Soon after the discovery of radioactivity in 1896 by Becquerel, Marie Curie and her husband Pierre discovered a new element which they named radium. They extracted dangerously large samples of radium from vast quantities of rock and experimented on its radioactive behaviour.

You could say: Radioactive atoms do not just stay there as atoms of ordinary copper do; they are completely different: they are unstable, they suddenly break up, flinging out a particle such as an alpha particle, becoming an atom of a different element.

A radium atom remains a radium atom, with the chemical behaviour of a heavy metal, until it suddenly hurls out this alpha particle. (The alpha particle has such a huge energy that it must come from the nucleus.) The remainder of the radium atom is no longer a heavy metal, but a quite different element. This ‘daughter’ of radium is an atom of a heavy inert gas, the end of the helium, neon, argon, krypton, xenon series. It is called radon. The atomic masses have been measured directly, radium-226, radon-222 (a difference of 4 suggesting that the lost alpha particle is a helium nucleus). Separate measurements confirm this.

When you have a mixture of a parent element and a daughter element which have different chemical properties, then they can be separated by ordinary chemical methods.

Radon gas is itself unstable and radioactive. Each of its atoms suddenly, at an unpredictable moment, hurls out an alpha particle. The remainder is a new atom, very unstable, which is called polonium, the ‘daughter’ of radon and the ‘granddaughter’ of radium. The series continues through several more radioactive elements and stops at a stable form of lead. The series does not begin with radium: it begins with uranium several stages earlier. Radioactive uranium (Z=92) has turned into lead (Z=82).

Making unstable atoms

A century ago, radioactivity was a peculiarity of a few mostly heavy, elements: the last few at the end of the Periodic Table. Nowadays scientists can bombard samples of lighter elements with high speed, high energy protons or neutrons, provided directly or indirectly by an accelerator. They can make unstable isotopes of every element in the periodic table. This has opened up the field of nuclear chemistry. Radioactive isotopes behave chemically like their stable isotopes and can be mixed with them. Their progress as radioactive tags can be traced, like luggage labels, following the progress of a ‘labelled’ isotope through the human body or an industrial process.

Half-lives

All the unstable members of these strange families have a constant, reliable characteristic: the atoms show no signs of ageing, or growing weaker, however long they last. Each radioactive element has a constant chance of breaking up in each succeeding second. This is described by a useful length of time, the ‘half-life’ of the radioactive element. For each individual atom the betting is 50:50 for and against its breaking up at any time during one half-life from now. The break-up seems to be controlled by pure chance. That chance does not change and make the break-up more likely for atoms that need to survive longer.

For radium the half-life is 1650 years. Start with 1000 mg of radium now and 1650 years later you will have only 500 mg left. After a further 1650 years only 250 mg will be left and so on. For radium’s daughter, radon -222, the half-life is 3.8 days. In less than four days half the radon gas will have disappeared. You will find helium gas there instead, with the solid products.

The instability appears to be something inherent in the nuclear structure. Nowadays, taking a wave view of the behaviour of nuclear particles, you can picture a stationary wave pattern defining the life of an alpha particle inside the nucleus. But the wave is not completely confined, it leaks through the potential barrier round the nucleus and runs on as a faint wave outside. The wave is interpreted as describing probabilities of locations. It is not a mechanical wave carrying energy and momentum.

While the alpha particle is expected to be found inside the nucleus, there is a chance of finding it one day outside, despite what would seem an insurmountable potential wall. That chance of the alpha particle being outside, being emitted, is definite and constant, a part of the defining wave property, as long as the nucleus lasts. It suggests that high energy alpha particles go with a short half-life of the parent nucleus.

One of the most important characteristics of radioactivity is that it decays exponentially. This has two basic mathematical implications at this level.

1. The rate falls by a constant ratio in a given time interval. The time it takes to fall by a half is always the same. It also falls to a tenth in equally regular, but longer, time intervals.
2. The rate of decay is proportional to the amount that is left. This can be seen in the experiment to model radioactive decay. The number of coins that decay in any ‘shake’ is proportional to the number that is left.

Radioactive decay experiment

From these features, you can argue, respectively, the following points.

• The chance of an atom disintegrating is constant in time. Radioactive decay is a series of many chance events, all with an unalterable chance.
• The rate of disintegrations is proportional to the total number of unchanged radioactive atoms at that moment. Both the rate and the stockpile itself die away exponentially with the same characteristic half-life.

The rate of decay of a radioactive source is proportional to the number of radioactive atoms (N) which are present.

dNdt = -λN

is the decay constant, which is the chance that an atom will decay in unit time. It is constant for a given isotope.

The solution of this equation is an exponential one where N₀ is the initial number of atoms present.

N = N₀e^-λ_t (Equation 1)

Constant ratio

This equation shows one of the properties of an exponential curve: the constant ratio property.

The ratio of the value, N₁, at a time t₁ to the value, N₂, at a time t₂ is given by:

N₁N₂ = e^-λt₁e^-λt₂

N₁N₂ = e^{-λ(t₁-t₂)}

In a fixed time interval, t₂ – t₁ is a constant. Therefore the ratio

N₁N₂ = a constant

So, in a fixed time interval, the value will drop by a constant ratio, wherever that time interval is measured.

Straight line log graph

Another test for exponential decay is to plot a log graph, which should be a straight line.

Since

N = N₀e^-λ_t

Taking natural logs of both sides:

lnN=lnN₀-λt

Therefore a graph of N against t will be a straight line with a slope of QuantitySymbol{-λ}.

Half-life and decay constant

The half-life is related to the decay constant. A higher probability of decaying (bigger λ) will lead to a shorter half-life.

This can be shown mathematically.

After one half life, the number, N of particles drops to half of N₀ (the starting value). So:

N = N₀2 when t=T_½

By substituting this expression in equation (see above),

N₀2 = N₀e^-λT_½

Taking natural logs of both sides gives:

ln½=-λT_½

ln2 = +λT_½

T_½ = 0.693λ

Countries have national laws to control how radioactive materials are acquired, used and disposed of. These laws follow internationally agreed principles of radiological protection.

The following principles apply to schools:

• There should be a person designated to be responsible for the security, safety and proper use of radioactive sources.
• Sealed radioactive sources should be of a safe design and type suitable for school science.
• Sealed sources should be used whenever possible in preference to unsealed sources. Unsealed sources can only be justified when the scientific demonstrations would not be practicable using sealed sources.
• Records of all radioactive sources should be properly kept, showing what they are, when they were bought, when and by whom they have been used, and eventually, how they were disposed of.
• Radioactive sources should be used only when there is an educational benefit.
• Radioactive sources should be handled in ways that minimize both staff and student exposures.
• Sealed sources should be carefully checked periodically to make sure they remain in a safe condition.
• The school should have a suitable radioactivity detector in good working order.

UK regulation & guidance

Generally, school employers will insist you obtain their permission before acquiring new radioactive sources.

You must follow your employer’s safety guidance relating to the use the radioactive sources. Most school employers will require you to use either SSERC or CLEAPSS safety guidance, as follows:

In Scotland, safety guidance for use of radioactive sources in schools is issued by the Scottish Schools Equipment Research Centre (SSERC) and is available to members through their website.

In the rest of the UK and British Isles Crown Dependencies, guidance is available from CLEAPSS, the School Science Service. Their guidance document, L93, is freely available from their website, even to non-members.

In the UK...

• In classes where children are under the age of 16, the use of radioactive material shall be restricted to demonstrations by qualified science teachers, (which includes newly qualified teachers). However, closer inspection of devices containing low-activity sources such as diffusion cloud chambers is permitted provided the sources are fully enclosed within the devices and not removed during the inspection.
• Young persons aged 16 and over may use radioactive sources under supervision. Although the use of radioactive material is regulated, it should not be used as an excuse to avoid practical work. As the ASE points out, "Using the small sources designed for school science gives a good opportunity to show the properties of radioactive emissions directly, and to discuss the radiation risks. Just as importantly, it is an opportunity to review pupils' perception of risks, as they are likely to have constructed their own understanding from a variety of sources, including science fiction films and internet sites. If the work is restricted just to simulations, it may reinforce exaggerated perceptions of risk from low-level radiation.”

Summary of legislation (UK)

Updated October 2008

The following summarizes the somewhat complicated legislative framework in which schools are expected to work with radioactive sources in the UK. However, teachers do not need to obtain and study this legislation; this has been done by CLEAPSS and SSERC, and it is incorporated into their guidance in plain English.

In the European Union, member states have implemented the 1996 EU Basic Safety Standards Directive (as amended) that in turn reflects the 1990 International Commission on Radiological Protection recommendations. In the UK, this has been done through the Radioactive Substances Act 1993 (RSA93), which controls the security, acquisition and disposal of radioactive material, and the Ionising Radiations Regulations 1999 (IRR99) which controls the use of radioactive material by employers. Transport of radioactive material is controlled by The Carriage of Dangerous Goods and Use of Transportable Pressure Equipment Regulations 2007.

There are exemptions from parts of the RSA93 and schools can make use of The Radioactive Substances (Schools etc.) Exemption Order 1963, The Radioactive Substances (Prepared Uranium and Thorium Compounds) Exemption Order 1962, and others. These exemption orders are conditional and to make use of them and avoid costly registration with the Environment Agency (or SEPA in Scotland, or the Environment and Heritage Service in Northern Ireland) you must adhere to the conditions. Note that currently, these exemption orders are being reviewed.

The way in which these laws are implemented in England, Wales, Northern Ireland and Scotland varies. The Department for Children, Schools and Families (DCSF) has withdrawn its guidance AM 1/92, and the associated regulations requiring this have been repealed. Consequently, purchase of radioactive sources by maintained schools in England is no longer regulated by the DCSF. The DCSF commissioned CLEAPSS to prepare and issue ‘Managing Ionising Radiations and Radioactive Substances in Schools, etc L93’ (September 2008) and has commended it to schools in England. Similar regulations relating to other educational institutions in the UK have not changed; English institutions for further education remain regulated through the Department for Innovation, Universities and Skills. Similarly, schools in Wales should follow the guidance from the Welsh Assembly Government Department for Children, Education, Lifelong Learning and Skills. Schools in Scotland should follow the guidance from the Scottish Government Education Directorate and associated guidance issued by SSERC. Schools in Northern Ireland should follow the guidance from the Department of Education Northern Ireland (DENI). The Crown Dependencies Jersey, Guernsey and Isle of Man are not part of the UK and schools and colleges should follow the guidance from their own internal government departments responsible for education.

In the UK, if an employer carries out a practice with sources of ionising radiations, including work with radionuclides that exceed specified activities (which is 100 kBq for Co-60, and 10 kBq for Sr-90, Ra-226, Th-232, Am-241 and Pu-239), the practice must be regulated according to the IRR99 and the employer must consult with a Radiation Protection Adviser (RPA). Since 2005, the RPA must hold a certificate of competence recognized by the Health and Safety Executive. Education employers are unlikely to have staff with this qualification, so the RPA will usually be an external consultant. Education employers need to notify the HSE 28 days before first starting work with radioactive sources. This is centralized at the HSE’s East Grinstead office.

Note: For higher risk work with radioactive material, the IRR99 requires designated areas, called controlled areas and supervised areas, to be set up if special procedures are needed to restrict significant exposure – special means more than normal laboratory good practice. It should never be necessary for a school to designate an area as controlled, and only in special circumstances would it be necessary to designate an area as supervised. The normal use of school science radioactive sources, including the use of school science half-life sources, does not need a supervised or controlled area.

Disposal of sources in the UK

Sources that become waste because they are no longer in a safe condition, or are no longer working satisfactorily, or are of a type unsuitable for school science, should be disposed of. In England and Wales, the Environment Agency has produced a guidance document through CLEAPSS that explains the available disposal routes. Similarly, SSERC has produced guidance for schools in Scotland. Schools in Northern Ireland should refer to DENI.

Health and safety statement

See the health and safety notes in each experiment. This is general guidance.

Health and safety in school and college science affects all concerned: teachers and technicians, their employers, students, their parents or guardians, and authors and publishers. These guidelines refer to procedures in the UK. If you are working in another country you may need to make alternative provision.