Bringing together two sets of constraints

Focusing on the learners:

Distinguishing–eliciting–connecting. How will you:

• develop the model of the nuclear atom
• maintain the connection between randomness for an individual nucleus and predictability over an ensemble
• keep the atomic electrons out of the model
• draw on existing understandings of energy to separate nuclear and atomic processes

Teacher Tip: These are all related to findings about children's ideas from research. The teaching activities will provide some suggestions. So will colleagues, near and far.

Focusing on the physics:

Representing–noticing–recording. How will you:

• separate transmutations from annihilations
• relate different representations of exponential decay
• relate emissions to transmutations
• explain why some nuclei are radioactive and some not

Teacher Tip: Connecting what is experienced with what is written and drawn is essential to making sense of the connections between the theoretical world of physics and the lived-in world of the children. Don't forget to exemplify this action.

The discovery of alpha, beta and gamma radiation

The initial discovery and identification of alpha, beta and gamma radiation provides an interesting case for how science works. The story takes us:

• From the initial discovery of the three kinds of radiation as a new phenomenon: this is something new!
• To the use of electric and magnetic fields in identifying the nature of the radiation: what is it?
• To theorising and experimenting on the origins of the new radiation: where does it come from and how is it produced?

Rutherford, Soddy, Villard and Becquerel: more depth

In 1898, Ernest Rutherford, then working at McGill University, Montreal, performed an experiment in which he placed successive layers of aluminium foil over a powdered uranium compound spread on a capacitor plate. A sensitive meter connected to the initially charged capacitor showed the rate of decay of charge from the capacitor as radiation from the uranium ionised the air between the plates. He found that the rate of ionisation decreased sharply on adding the first few layers of aluminium and then very slowly with additional layers. This finding led Rutherford to conclude that the radiation from the uranium consisted of two components: one capable of penetrating only a few centimetres of air or a few layers of aluminium foil and the other capable of penetrating much greater thicknesses of air or aluminium. Rutherford suggested that the two types of radiations should be designated alpha and beta. In 1900, the Frenchman, Villard, discovered a third, still more penetrating component, which he referred to as gamma radiation, following Rutherford's lead.

At this time the identity of these three kinds of radiations was unknown and investigations concentrated on finding out about the rays by passing them through electric and magnetic fields. In 1899, Becquerel showed that a component of the radiation from radium was deflected by electric and magnetic fields, as would be expected for negatively charged particles. Further experiments with electric and magnetic fields showed that this radiation was the same as Rutherford's beta rays, consisting of streams of high-velocity electrons. At first it was thought that neither alpha nor gamma radiations were deflected by electric and magnetic fields. In 1903, however, Rutherford showed that when using sufficiently strong electromagnets, alpha radiation is deflected as though positively charged. These alpha particles were later identified as being doubly ionised helium ions, while gamma radiation was identified as being high-frequency electromagnetic radiation.

Identification of the three forms of radiation, by using electric and magnetic fields, gave no insight into the origin of the radiation. The big question remained: how could the continuous emission of particles/radiation in the absence of chemical triggers or other alterations in the state of the radioactive materials be accounted for? It was well known that changing the ambient temperature and pressure of a chemical reaction changes the rate of reaction, and numerous efforts were made to determine whether such changes had any effect on the intensity of radiation from various sources. No effect was observed.

These findings led Rutherford and Soddy, in 1902, to the conclusion that: Since…radioactivity is at once an atomic phenomenon and accompanied by chemical changes in which new types of matter are produced, these changes must be occurring within the atom, and the radioactive elements must be undergoing spontaneous transformation. The results have so far been obtained, which indicate that the velocity of this reaction is unaffected by the physical and chemical conditions, making it clear that the changes in question are different in character from any that have been before dealt with in chemistry. It is apparent that we are dealing with phenomena outside the sphere of known atomic forces. Radioactivity may therefore be considered as a manifestation of subatomic chemical change. (Philosophical Magazine, September, 1902).

In the following years, this theory, involving the spontaneous emission of radiation from the nuclei of certain atoms and the consequent transformation of those atoms from one element to another, was fully substantiated.

Making the wrong connections in thinking about the production of gamma radiation

Wrong Track: Gamma radiation is a form of electromagnetic radiation. It must be produced in the same way as radiation such as ultraviolet which is given out when electrons outside the nucleus fall from a higher to a lower energy level.

Right Lines: Gamma radiation originates in the nucleus of atoms and is often produced alongside alpha and beta radiation. When a nucleus emits an alpha or beta particle, the daughter nucleus is usually left in an excited state. It can then move to a lower energy state by emitting a gamma ray. This is similar to the way in which an atomic electron (outside the nucleus) jumps to a lower energy state by emitting infrared, visible or ultraviolet light.

Making the wrong connections in thinking about the production of beta radiation

Wrong Track: Beta radiation consists of electrons, and electrons come from the atomic orbits outside the nucleus.

Right Lines: Beta radiation originates in the nucleus of the atom. In beta emission a neutron within the nucleus is converted into a proton and an electron, and the electron is emitted.

Effect of temperature and pressure on radioactive sources

Wrong Track: If you heat up a radioactive source, such as radium, it will become more active and give out radiation at a greater rate. It's just the same as with heating up chemicals in chemical reactions.

Right Lines: Changing the temperature of a radioactive source has no effect on the activity of the source.

Radioactivity is different from chemical change

Thinking about the teaching

The fundamental point to stress here is that external conditions, such as temperature and pressure, have no effect on the activity of a radioactive source. The spontaneous emission of radiation involves changes within the nucleus of each atom of the source. This is a different process from that involved in chemical changes where increasing the temperature results in increased motion of atoms, more frequent collisions and a consequent increased rate of reaction.

Why are they called nuclear power stations?

The phenomenon of radioactivity is due to changes in the nucleus of each atom of a radioactive material. It is for this reason that we refer to:

• Nuclear weapons
• Nuclear power stations
• Nuclear reactions
• Nuclear energy

For some students this point may not be obvious:

Karl: Why are they called nuclear power stations? I thought it was to do with radioactivity!

Teacher: Nearly right! It is to do with radioactivity. Radiation is emitted from the nucleus of the atoms in fuels for these power stations and enables more nuclear emissions. That's why we call them nuclear reactors or nuclear power stations.

From time to time it is a good idea to refer to nuclear alpha/beta/gamma radiation or nuclear ionising radiation just to remind students of their origin.

How can radioactive decay be both random and based on fixed chance?

Wrong Track: How can it be possible for radioactive decay to be random and yet based on fixed chance at the same time? If the process is random you can't predict it and if it has a fixed chance you can!

Right Lines: If you imagine a stockpile of atoms making up a radioactive source, it is not possible to predict which atomic nucleus will disintegrate next but there is a fixed chance of disintegration, which applies to all of the atoms.

Modelling radioactive decay with dice

Thinking about the learning

For some students the idea that the process of radioactive decay can be both a random process and one subject to fixed chance may seem strange.

Thinking about the teaching

Experience shows that it is really helpful to model radioactive decay by using a simple dice simulation. In one form of the activity, each student in the class is given 20 dice (radioactive atoms) and all students shake and roll their dice together. A six is taken to indicate the disintegration of an atom and each time a six appears that dice is removed. The remaining stockpile of radioactive dice, summed after each throw across all students, follows an exponential decay curve. This activity clearly models the random nature of the event (it's not possible to predict which dice will disintegrate next) along with the underlying fixed chance (one in six) of decay.

We'd suggest emphasising that it's a constant fraction that decay – here one-sixth. This constant-fractional-decay is the key idea.

Piles of nuclei: changing but not being removed

It's quite helpful to get students to visualise radioactive decay in terms of a stockpile of atoms containing nuclei. The word stockpile fosters an image of a pile of atoms. This remains constant, but the nuclei inside the atoms are transmuted, and so the atoms are transmuted. During radioactive decay, the number of atoms stays constant but the number of nuclei of any sort can vary with time. If you're focusing on a single-step decay then the stockpile of nuclei you start off with will gradually get depleted (stock levels of that kind of nucleus go down: stock levels of all kinds of nuclei are constant).

Teacher Tip: Some things (the numbers of particular kinds of nuclei) change; some stay the same (the total number of nuclei). Apples do change to oranges, but here the number of pieces of fruit stay the same.

This is, of course, very different from fission and fusion, where nuclei split or join. The number of atoms will therefore change.

Modelling radioactive decay with dice: unintended outcomes!

Wrong Track: When the nucleus decays, it disappears like with the dice. You have to remove each dice when it comes up as a six so the stockpile of atoms goes down.

Right Lines: When a nucleus decays, it changes its composition but the nucleus still remains. For example, when a nucleus emits an alpha particle, it loses two protons and two neutrons but the rest of the nucleus is left behind.

A limitation of the dice model

Thinking about the teaching

This is an interesting point relating to the limitations of models, which we'd recommend exploring in full with the students:

Teacher: Just think back to what you were doing with the dice. Each time an atom came up as a six, it meant that it had disintegrated, giving out radiation. That atom was then removed from the stockpile of radioactive dice.

Teacher: Can anyone see how this model of radioactive decay differs from what happens with a real radioactive source such as uranium?

Jade: It's not really that the atoms are removed once they have given out radiation.

Teacher: Yes, keep going, you're on the right lines …

Jade: Well, in the model you take the atom away when it gives out radiation. That doesn't happen in real life, otherwise you'd end up with almost nothing there. Each uranium nucleus just loses some particles but most of it is still left behind.

Teacher: Great answer! Perhaps we should just put the disintegrated dice to one side to indicate that they are now stable, but are still there.

Highlighting a new form of change

Radioactive decay may well be the first example that students meet of an exponential change. It is therefore important to draw attention to this new form of change:

Teacher: So, if we look at the activity curve for the radioactive source, what can we say about its shape?

Abdul: It goes down.

Teacher: Yes, it goes down! How does it go down?

Nicki: Steeply at first and then more gently.

Teacher: Exactly right! Who can explain this pattern? Think about the activity we did with the dice.

Azul: At first there are lots of radioactive atoms… so you are more likely to get a six!

Teacher: Well, that's right. At first there are lots of unstable atoms, that decay with a fixed chance, and as time goes by the remaining stockpile of atoms gets smaller and so the rate of decay (or the number of sixes) gets smaller.

Making links between different representations

A key part of learning physics involves making links between different representations. This is certainly the case for radioactive decay. In building up a picture and understanding of radioactive decay, students are required to move between a range of different representations.

• The physical process: students watch a demonstration carried out by the teacher of the decay of a radioactive source (with a short half-life). They become aware of the falling off in the counting of the Geiger–Müller tube: steeply at first and then more slowly.
• A graphical representation: the students plot a graph of the activity of the source against time.
• A physical model: the students work with a dice model of radioactive decay.
• A mental model: the teacher encourages students to visualise a stockpile consisting of two colours of balls. Over time, one colour changes to another.
• A mathematical model: the students carry out calculations based on the constant fractional decay of the radioactive source.

Meaningful learning by students comes about when they are able to link, and move easily between, all of these processes, models and representations.

What halves during a half-life?

Wrong Track: If the half life of a radioactive source is 100 years, this means that half of the source will decay away in that time. If you have 10 gram of material at the start there will be 5 gram left after 100 years.

Right Lines: If the half-life of a radioactive source is 100 years, this means that half of the radioactive atoms will decay in that time but the source will undergo no significant change in mass.

If we start with 10 gram of a radioactive source…

Thinking about the learning

What halves during a time period of one half-life? This thinking that underpins this challenge relates closely to the challenge Does a nucleus disappear when it decays?

Thinking about the teaching

It is worth addressing this issue directly:

Teacher: So if we start with 10 g of an alpha emitting radioactive source what will be its mass be after one half-life?

Bill: 5 g.

Teacher: No, in fact that's not correct. There's virtually no change in mass of the source. Who can explain why? You need to think carefully about this.

Simon: You might think it's 5 g but it isn't because when the radioactive atoms decay they don't disappear, they just change into different atoms.

Teacher: Great explanation! Out of interest how much mass will be lost from the source?

Sarah: The total mass carried away by the alpha particles. You lose two protons and two neutrons with each alpha particle.

Teacher: That's pretty much all of it. In nuclear reactors you also lose a tiny fraction of the mass – in exchange for a lot of energy in a thermal store.

There's a good chance you could improve your teaching if you were to:

Try these

• dealing with the properties of ionising radiations before dealing with the sources
• building up a simplified model of the atom, as needed
• introducing a wide variety of sources, not only nuclear
• building and discussing models of exponential decay
• relating emissions to transmutations
• exploiting a good model of energy, discussing changes in the nuclear store

Teacher Tip: Work through the Physics Narrative to find these lines of thinking worked out and then look in the Teaching Approaches for some examples of activities.

Avoid these

• not drawing attention to the vastly different energies of photons with nuclear and atomic origins
• not emphasising the nuclear origins of the ionising emissions
• using the term atomic power
• keeping the different representations of exponential decay separate, rather than relating them
• avoiding negative energy, when accounting for nuclear transformations

Teacher Tip: These difficulties are distilled from: the research findings; the practice of well-connected teachers with expertise; issues intrinsic to representing the physics well.