Arriving photons fill a store, drip by drip

When photons are absorbed there is always some change in the absorber. Absorption is the end for the photon: it is destroyed and the energy it was shifting is made available to the absorber. As a result of this new supply of energy, new processes are made possible in the absorber. Exactly what these are depends on the absorber. In episode 02 you saw how the interactions of photons and matter depended on both the energy (and so the frequency) of the incident photon, and on the material of the absorber. Two kinds of interactions were introduced: threshold and lock-and-key. Here we'll concentrate on developing the model of the atom a little, so that the you can develop an energy-based account of what happens during absorption. We'll start with the lock-and-key account.

It's a fact that only certain frequencies are absorbed by particular materials. So only certain quantities of energy are absorbed: larger or smaller amounts, corresponding to higher or lower-frequency photons, are rejected. So whatever model we build of the atom, as the constituent of the absorbing material, will be quantum in nature, as the photon is quantum in nature. The mechanics of atoms, developed in the early 20th century, was quantum mechanics. This is rather complicated and involves some behaviour that is very different from the world at the scale of humans (a few metres and a few seconds). This should not be so surprising as the scale of atoms is a thousand million times smaller (a few nanometres). Here we'll aim for a suggestive, rather than a comprehensive, model but with no deliberate dead-ends embedded in the model.

You should also be pretty confident with the idea, from earlier work on ionisation, that the atoms contain both positive and negative charged particles. That might give the beginnings of a model with which to think about the energy: if these charged particles have their separation altered then the energy in the electromagnetic store is changed. This can work both ways: if the separation between the oppositely charged particles is reduced by a discrete amount then the energy in the electromagnetic store is depleted by a corresponding discrete amount, and this could correspond neatly with the discrete energy shifted by an emitted photon. Conversely, the separation between the oppositely charged particles could be increased by a discrete amount then the energy in the electromagnetic store is augmented by a corresponding discrete amount, and this could correspond neatly with the discrete energy shifted by an absorbed photon.

This is neat and leaves only the small challenge of a plausible mechanism to explain why only certain separations of the charged particles seem to be permitted. This certainly is a topic for further study, involving wave mechanics, so much of the work in this topic will be useful to make a start in that area, but the mathematics is quite hard, so we don't make any progress along that route here. It took very smart people some time to develop a mechanism, and even then, almost a century on, there is still debate about how we should interpret that mechanism, as it has such apparently counter-intuitive implications.

A simple model describes each element as an energy map: a one-dimensional chart of the energy that can be stored (the energy levels). Each kind of atom is distinct (it's a separate element), and so has its own distinctive map. Indeed, these maps are like fingerprints, serving to identify the atoms. The identification takes place remotely: simply look at the discrete frequencies (and so colours) that are emitted or absorbed by the atom. This quiver of photons will uniquely identify the atom, wherever it is in the universe.

A photon absorbed: energy stored in the atom.

A photon emitted: energy released from the store in the atom.

Up and down the ladder of energy

The components of an atom are not static, and what has been learnt about atoms over the last 100 years suggests that simple static pictures are simply misleading.

So picturing the negatively charged particles in atoms, electrons, as small hard spheres with a minus in the middle somewhere is not helpful. Adding an orbital motion about the positively charged particles concentrated in the nucleus does not make the picture any more helpful.

The energy ladder picture is both economical and precise. Adding the idea that this energy is stored by separating the positively and negatively charged particles, so the electrons move further away from the nucleus, is generally true and adds an ability to visualise a physical arrangement that might underpin the energy description, but at the risk of being correct in only some cases. Quantum mechanics, the most tested theory of the atom that we have, treats the electron as a delocalised entity, so any simple picturing will not do. So we suggest that you avoid diagrams that seek to be a more literal picture of the situation. It turns out that the resources at our disposal for making images of the world garnered from illustrating and otherwise representing scenes at scales of millimetres to kilometres just do not work at the scale of nanometres: the world down there is very different.

But arriving photons do change the absorber, firstly by altering the energy stored in the atom by rearranging the outlying constituents of the atom – the electrons. This depends on the lock-and-key mechanism by which photons shift energy to or from the atom's store. The second way in which they can change the absorber is through the threshold effect, where the energy provided is enough to lift the electron right off the top of the energy ladder and so ionise the atom.

To lift the electron right out of the atoms requires more energy: the photons must be more energetic to ionise the absorber. The only difference between ionising and non-ionising photons is frequency. Higher-frequency photons shift more energy on interaction, and so are able to strip electrons from atoms, leaving ions behind.

Activity and absorption: fixed chance of absorption for each thickness

Photons passing through a thickness of absorber have a fixed chance of being absorbed. This reduces the activity of the beam, but also brings changes in the absorber. These changes can be exploited to detect the photons in the beam: you just tune the material or structure of the absorber to get a particular change triggered by the absorption, then look for that change.

However, as the pattern of absorption shown here makes plain, the number of changes that you get depends on the initial activity of the beam; the material of the absorber; and the thicknesses of absorber already traversed.

The pattern of absorption is also important when considering safety, as the activity of the beam is only reduced by a constant fraction as each additional slice of absorber is added. This fraction can be altered by increasing the thickness of each slice or altering the material from which the slices are cut.

Ionising: any way of increasing the energy in the store will do

It's not only photons that can ionise. What's needed to produce an ionisation is some way of augmenting the energy store of an atom so that the electron can be stripped from that atom, climbing off the top of the energy ladder. Fast-moving, small, charged massive particles are another effective way of supplying the required energy.

The fast moving and massive facets ensure that the particles have energy in their kinetic store to shift to the stores of the atoms. Why small? Well, the delivery needs to be to individual atoms, so the collision needs to be with a single atom and not with a whole surface composed of many atoms. And charged – that's again not so hard: the passing, fast-moving, particle must exert a force on the charged parts of the atom in order to rearrange them, and electric forces are large enough to do this in the short time available. Some of the energy in the kinetic store of the particle is shifted as a result of this interaction: the particle is slowed down. This is very different from the photon, where the photon is destroyed as it ionises an atom.

As the ways in which atoms are ionised are very different for particles and photons, so the distribution of energy through the material is very different. This has consequences for safety and for therapeutic applications of ionising radiation.

How to detect ionising radiations

Both photons and particles can shift enough energy to to convert the absorber atoms to ions. Detect these ions and you'll have a way of detecting the radiation. Atoms are neutral and ions are not, so exploit the newly made charged particles by constructing a detector around a carefully arranged absorber.

Historically there were two common ways of exploiting these newly produced charged particles: one makes sparks; one makes clouds. Each detects the radiation indirectly, from the trail of charged particles that it leaves behind.

To make sparks, accelerate the ions (arrange for an electric force to be acting on them) and allow these ions to accumulate a large speed before striking another atom (so keep the atoms far apart – make the absorber a gas). This target atom is in turn ionised (it's struck by a fast-moving charged particle – a familiar process). Allow the cascade to continue. When enough ions are moving you'll have a spark.

To make clouds, arrange the absorber to be a very wet atmosphere, where the slightest disturbance will produce a cloud. The ions provide that disturbance, as the surrounding molecules are attracted to the charged particles, which form condensation nuclei – the small disturbances necessary for the droplets that make up clouds. Jet contrails on a clear day are perhaps the most visible example of disturbances producing a cloud, although these are sudden changes in pressure, not trails of ions.

Different detectors have different advantages (and so comparative disadvantages)

Making clouds shows you where the particles have been – it reveals their paths. These are cloud chambers, and they retain a usefully physical link to the events that caused the cloud. It's easy to imagine the small charged particles tracking through the absorber and leaving a trail of ionised atoms in their wake. Bubble chambers were a development that followed the same principles, but with higher resolution, but they have in turn been superseded by techniques that can more easily dump the large quantity of data now generated by studies of ionising radiations into a computer for preliminary analysis. Bubble chamber photographs had to be hand traced. Also, finding the beam activity from these trails is hard work, because you have to count the trails.

Spark counters developed into (sealed) Geiger–Müller tubes, which are probably what you use to detect radiation in a school laboratory. They are good for counting, but you need an array of such spark counters to see the path the particle took.

For both kinds of detector it is unwise to assume that all kinds of radiation will be detected equally. Gamma does not make enough ions per millimetre to make clouds, and Geiger–Müller tubes may only detect 1 in every 10 000 that pass through the tube. Alpha radiation makes so many ions per millimetre that the walls of the Geiger–Müller tube may absorb all the alpha radiation before it reaches the gas molecules that the design relies on them ionising. As with many measurements in physics, skill, care and perseverance is needed to ensure that you have measured what you thought you had.

Fast-moving charged particles ionise effectively

Fast-moving charged particles can rather easily shift energy to atoms and so strip electrons – that is, ionise the atoms. There is a force between the charged particle and the charged particles in the atoms that is large enough to shift lots of energy to the store associated with the atom. The larger this force, the more energy that can be shifted during the short time for which the fast-moving particle is close to the atom. The size of the force depends both on the charged particles (on the passing particle and the charged particles in the atoms) and on the distance between them (see the SPT: Forces topic). Since atoms have their positive charge concentrated in the centre shielded by the surrounding electrons, and it's the electrons that are to be stripped from the atom, so the charge at one end of the interaction are always the same: the charge on an electron. At the other end the charge will depend on the ionising particle.

Remembering that the larger the charge, the larger the force, you can see that particles with larger charges are likely to be more ionising. If they also have a larger mass, then they will be deflected less by the force of the interaction, and so remain closer to the atom for longer. So it is that high mass, highly charged particles do a lot of damage. But there is an upside: each joule of damage done is a joule shifted from the kinetic store of the particle, so slowing it down. Such particles therefore tend to be short range, as the energy in their kinetic store is dissipated rather rapidly.

Lower-mass, less highly charged particles may do less damage per millimetre of absorber traversed, but they do travel further, and so may be more dangerous for biological tissue, as they do manage to travel from the source through the air, and get as far as the tissue, rather than only ionising the air and puttering to a halt before they reach it.

So what are the more common particles we actually find?

History plays a part here, as the first two letters of the greek alphabet were used to name the first two ionising charged particles that were detected: alpha and beta. Later this pair were shown to be nuclear in origin (more on this in episode 05), and so described by reference to what could be found in nuclei. It turns out that the alpha particle has the same charge and mass as a helium nucleus, and the beta particle the same charge and mass as an electron. Putting this together with the discussion about the factors that affect ionising, you'd expect the alpha particle to be the short-range, highly ionising radiation, and the beta particle to be the longer-range radiation, and, as a consequence, ionising rather less for each millimetre traversed. The energy in the kinetic store as the radiation is emitted sets the range: the discussion so far alters the rate at which that store is depleted. Here again there is a difference between the two kinds of radiation: beta particles are emitted with a range of energies from a single source, typically varying from some maximum down to zero. Across different sources the maximum energy varies from 3 attojoule–3 picojoule (300 aJ–3 picojoule). Alpha particles, by contrast, are all of the same energy from a given source (mono-energetic), and this energy varies from 0.4–1.0 picojoule. Alpha particles are much more damaging than beta because:

• They shift more energy to the target per millimetre (more charge and more mass).
• There is more energy in their kinetic store to shift.

The third kind of ionising radiation to be discovered was named gamma, after the third letter of the greek alphabet, and it turned out to have no mass and no charge. In fact, it's the photon, but this time a very-high-frequency example, and again emitted from the nucleus (again, more on this in episode 05).

Detecting alpha, beta and gamma radiations

These are the three traditional types of radiation, and it is easily possible to distinguish between them because they have very different charges and masses, as well as differing in their typical ionisation per millimetre of absorber, and so in their range.

The varying charge results in differing forces when they are placed in an electric field. These forces produce varying accelerations, depending on the mass of the particle. The accumulated velocities from these accelerations lead to varying paths, which can be detected.

The movement of the positive or negative charges results in a current – a flow of charges. These currents are anti-parallel for the alpha and beta particles and so result in forces in opposite directions when the particles pass through a magnetic field. Again, the differing masses affect the resulting accelerations, and the curvature of the tracks enables the experimenters to distinguish between the particles.

The same techniques are used in distinguishing between the many other ionising particles of nuclear origins that have been detected and identified in the century following the first discovery of these particle-like ionising radiations: protons, neutrons, positrons, and many others. The detectors built into the LHC use these same techniques to work out what is produced in the very energetic collisions between the two beams of particles.

Activity, count and dose are different measures

Counting the arrival of ionising radiations is a cumulative affair – the result is an ever-increasing number. Just count the blips as a result of activity in a Geiger–Müller tube – or tally up the number of tracks in a cloud chamber. The count is the accumulation of the activity of the beam over time. So far we have focused on activity, as this is proportional to power in the beam, which is more focused on our immediate interests for many radiations. However, the cumulative effect of ionising radiation is significant, as the damage done to the absorbing material depends on both activity and time.

The activity of a source is measured and quoted in bequerels (Bq), where one bequerel is 1 emission per second. As is common with units, this one is named after a scientist who did significant work on the topic, Henri Bequerel (1852–1908). The measure of the count rate will probably be lower, as we have seen, for all kinds of reasons: some radiations will not be detected as the detector will not be triggered by them (for example, not enough ions produced to generate a spark); some will be absorbed before arriving at the detector and some will miss the detector altogether. Once such allowances have been made, the count is simply the accumulation of (activity  ×  time). (The bequerel replaces the older unit of the curie, which is 3.7 × 10¹⁰  events per second. You may still find that many school sources are marked up in microcurie – that is, millionths of a curie.)

Often the concern is with the interaction of ionising radiation with biological tissue, which can self-repair but only over moderate timescales. So the rate at which the damage is done remains important: just knowing about the accumulated count is not enough. Indeed, there are many uncertainties about what the effects of exposure to beams of particular activities are, which makes it rather hard to reliably estimate risks and to offset them against benefits.

Dose and damage are different but related: they have different measures

As you've already seen in episode 02, the interaction of photons with matter is not that simple. The material significantly affects the likelihood of the photon interacting as it passes through each millimetre of material. This is true even for threshold effects. So both for applications, where objects are purposefully irradiated, and for precautionary steps, where we want to limit the exposure of given slices of absorber to ionising radiations, there are other measures that incorporate more experimental knowledge of how the radiation interacts with the material.

The first of these is the gray (Gy). This is rather simple and important, because it measures the energy shifted by the radiation to each kilogram of absorber. As the damage done by the radiation is by shifting energy to strip electrons from atoms, it is easy to see that this is an important measure. Three beams, of alpha, of beta or of gamma radiations, each striking an absorber, will shift different quantities of energy to the successive slices through which they pass, because they all ionise in different ways. Indeed gamma, being essentially a photon, will show a very different pattern of ionisation, slice by slice, from the other two as they shift most energy when travelling slowest, towards the end of their passage through the slices. The pattern of ionisation by photons is one of constant fractional decay, as you noticed earlier. In the treatment of a cancer, the radiologist aims to shift 20–80 gray to the cancer in order to damage it fatally.

Biological tissue varies in its response to radiation, and there is a measure which incorporates empirical constants to capture this data. This is the sievert (Sv). It modifies the dose in gray using two factors: one for the kind of radiation (for all photons this is 1), and one for the tissue. Since the measure compares the effect of the radiation to that of being irradiated by photons, it is called the dose equivalent: that is equivalent to being irradiated by photons. A typical natural environmental exposure over the whole year is about 2 millisievert (2 mSv).

Energy in measured joules, but other units are sometimes convenient and so still in use

Energy is measured in joule – except when it's not. For historical reasons there are a number of other measures of energy for ionising radiations. Foremost among them is the electron-volt.

You'll often find the energies of, say, alpha particles measured in mega electron volt (MeV).

Electrons have a charge. The SPT: Electricity and energy topic shows how to calculate the energy shifted by a charge moving through a potential difference.

energy shifted = charge × potential difference

1 electron-volt is 1.6 × 10^-19 joule

1 MeV is 1.6 × 10^-13 joule.

Here we'll prefer joule. Alpha radiations from a particular source are mono-energetic: they are all emitted with a single energy.

Here are a sample range of values, for emissions from different nuclei: U₂₃₅, 706.4 femtojoule ; Ra₂₂₅, 713.6 femtojoule ; Hf₁₇₄, 400.0 femtojoule . (These are quoted in femtojoules, where 1 femtojoule is 1.6 × 10^-15 joule.)

Thicker is safer, as activity is reduced by a constant fraction for each additional thickness

If you want to be safe from those ionising photons then there is no substitute for plenty of absorber atoms between you and the source. You can increase the number of atoms in two ways: use denser materials (so more particles per cubic metre) or place a greater thickness of absorber between you and the source. So either change the material of which the protective absorber is made or place more slices of material between you and the absorber.

Each slice absorbs a given fraction of the photons. This is a consequence of a fixed probability that each photon is absorbed on its passage through each millimetre of absorber. Averaged over the many photons in a beam, this produces a constant fractional decay. This kind of decay is an important pattern in mathematics, and one that rather commonly occurs in nature. This is an exponential variation, here with the thickness of absorber traversed.

How the activity varies: exponential variation with distance

The exponential pattern is one that has a signature: each increment in the independent variable produces the same fractional change in the dependent variable. This is always true: for radiations you'll see this where the independent variable is thickness (here) or time (to come in episode 05). One significant fractional change is a halving. So for radiations you'll often see the half-thickness quoted: the thickness of absorber required to reduce the number of photons incident on the front face of the slice by 50 % before they exit through the back face of that slice. For the photons used for medical X-rays, the half thickness for lead is about 0.5 millimetre. However, photons with energy five times as high have a half thickness of 10 millimetre of lead, or 50 mm of concrete.

Start with 1 024 000 high-energy photons.

• After 50 mm of concrete there will be 512 000 photons.
• After 100 mm of concrete there will be 256 000 photons.
• After 150 mm of concrete there will be 128 000 photons.
• After 200 mm of concrete there will be 64 000 photons.

Is this safe? How much more concrete must you use to be safe? Is there a completely safe?

The law of diminishing returns ensures that there is no such thing. There is a balance to be struck.

A unified view of ionising radiations

An atom or molecule is ionised by having at least one electron stripped from it:

atom  →  ion + electron

or

molecule  →  ion + electron.

In both cases, energy must be shifted to the atom to allow the change. One way to shift that energy is by ionising radiation striking the neutral particle. This can be either high-energy (and so high-frequency) photons or fast-moving massive particles (so with energy in their kinetic store to ionise the atoms).

Radiations that ionise and the units that are used to measure their effects

Detecting the ions produced in the absorber is a way of detecting the arrival of ionising radiation.

The rate at which the radiation is emitted is the activity, measured in bequerels.

The energy shifted to each kilogram of absorber is the dose, measured in grays.

The damage done by the dose is measured in sievert.

The dose to a particular target can be controlled by varying the thickness of absorber between the source and the target, the material from which the absorber is made and the energy of the radiations emitted from the source.