by Frank Close
We can sense the electromagnetic spectrum beyond the rainbow; our eyes cannot see infrared radiation but the surface of our skin can feel it as heat. Modern infrared cameras can ‘see’ prowlers by the heat they give off. It is human genius that has made machines that can extend our vision across the entire electromagnetic range, thereby revealing deep truths about the nature of the atom.
Our inability to see atoms has to do with the fact that light acts like a wave and waves do not scatter easily from small objects. To see a thing, the wavelength of the beam must be smaller than that thing is. Therefore, to see molecules or atoms needs illuminations whose wavelengths are similar to or smaller than them. Light waves, like those our eyes are sensitive to, have wavelength about 10–7 m (or put another way: 10,000 wavelengths would fit into a millimetre). This is still a thousand times bigger than the size of an atom. To gain a feeling for how big a task this is, imagine the world scaled up 10 million times. A single wavelength of light, magnified 10 million times, would be bigger than a human, whereas an atom on this scale would extend only 1 millimetre, far too little to disturb the long blue wave. To have any chance of seeing molecules and atoms we need light with wavelengths much shorter than these. We have to go far beyond the blue horizon to wavelengths in the X-ray region and beyond.
X-rays are light with such short wavelengths that they can be scattered by regular structures on the molecular scale, such as are found in crystals. The wavelength of X-rays is larger than the size of individual atoms, so the atoms are still invisible. However, the distance between adjacent planes in the regular matrix within crystals is similar to the X-ray wavelength and so X-rays begin to discern the relative position of things within crystals. This is known as ‘X-ray crystallography’.
An analogy can be made if one thinks for a moment of water waves rather than electromagnetic ones. Drop a stone into still water and ripples spread out. If you were shown an image of these circular patterns you could deduce where the stone had been. A collection of synchronized stones dropped in would create a more complicated pattern of waves, with peaks and troughs as they meet and interfere. From the resulting pattern you could deduce, with some difficulty admittedly, where the stones had entered. X-ray crystallography involves detecting multiple scattered waves from the regular layers in the crystal and then decoding the pattern to deduce the crystalline structure. In this way, the shape and form of very complicated molecules, such as DNA, have been deduced.
To resolve the individual atoms we need even shorter wavelengths and we can do this by using not just light, but also beams of particles such as electrons. These have special advantages in that they have electric charge and so can be manipulated, accelerated by electric fields, and thereby given large amounts of energy. This enables us to probe ever shorter distances, but to understand why we need to make a brief diversion to see how energy and wavelength are related.
One of the great discoveries in the quantum theory was that particles can have wavelike character, and conversely that waves can act like staccato bundles of particles, known as ‘quanta’. Thus an electromagnetic wave acts like a burst of quanta – photons. The energy of any individual photon is proportional to the frequency (ν) of the oscillating electric and magnetic fields of the wave. This is expressed in the form
E = hν
where the constant of proportion, h, is Planck’s constant.
The length of a wave (λ), and the frequency with which peaks pass a given point, are related to its speed, c, by ν = c/λ. So we can relate energy and wavelength
and the proportionality constant hc ~ 10–6 eV m. This enables us to relate energy and wavelength by the approximate rule of thumb: ‘1 eV corresponds to 10–6 m, and so on.
5. Energy and approximate wavelengths.
You can compare with the relation between energy and temperature in Chapter 2, and see how temperature and wavelength are related. This illustrates how bodies at different temperatures will tend to radiate at different wavelengths: the hotter the body, the shorter the wavelength. Thus, for example, as a current flows through a wire filament and warms it, it will at first emit heat in the form of infrared radiation – and as it gets hotter, a thousand degrees or so, it will begin to emit visible light and illuminate the room. Hot gases in the vicinity of the Sun can emit X-rays; some extremely hot stars emit gamma rays.
To probe deep within atoms we need a source of very short wavelength. As we cannot make gamma-emitting stars in the laboratory, the technique is to use the basic particles themselves, such as electrons and protons, and speed them in electric fields. The higher their speed, the greater their energy and momentum and the shorter their associated wavelength. So beams of high-energy particles can resolve things as small as atoms. We can look at as small a distance as we like; all we have to do is to speed the particles up, give them more and more energy to get to ever smaller wavelengths. To resolve distances on the scale of the atomic nucleus, 10–15 m, requires energies of the order of GeV. This is the energy scale of what we call high-energy physics. Indeed, when that field began in earnest in the early to middle of the 20th century, GeV energies were at the boundaries of what was technically available.
By the end of the 20th century, energies of several hundred GeV were the norm, and we are now entering the realm of TeV scale energies, probing matter at distances smaller than 10–18 m. So when we say that electrons and quarks have no deeper structure, we can only really say ‘at least on scales of 10–18 m’. It is possible that there are deeper layers, on distances smaller than these, but which are beyond our present ability to resolve in experiment. So although I shall throughout this book speak as if these entities are the ultimate pieces, always bear in mind that caveat: we only know how Nature operates at distances larger than about 10–18 m.
Accelerating particles
The ideas of accelerators will be described in Chapter 5, but for the moment let’s reflect a moment on what is required. To accelerate particles to energies of several tens or hundreds of GeV requires lots of space. Technology in the mid- to late 20th century could accelerate electrons, say, at a rate corresponding to each electron in the beam gaining some tens of MeV energy per metre travelled. Hence at the Stanford Linear Accelerator Center in California (SLAC) there is a 3-km-long accelerator which produced beams of electrons at up to 50 GeV. At CERN in Geneva, the electrons were guided around a circle of 27 km in length, achieving energies of some 100 GeV. Protons, being more massive, pack a bigger punch, but still require large accelerators to achieve their goals. Ultimately it is the quantum relation between short distances, the consequent short wavelengths needed to probe them, and the high energies of the beams that creates this apparent paradox of needing ever bigger machines to probe the most minute distances.
These were the early aims of those experiments to probe the heart of the atomic nucleus by hitting it with beams of high-energy particles. The energy of the particles in the beam is vast (on the scale of the energy contained within a single nucleus, holding the nucleus together), and as a result the beam tends to smash the atom and its particles apart into pieces, spawning new particles in the process. This is the reason for the old-fashioned name of ‘atom smashers’. Today we do much more than this and the name is defunct.
The electron and proton
The electrically charged particles that build up atoms are the electron and proton. An atom of the simplest element, hydrogen, consists normally of a single electron (negatively charged) and a proton with the same amount of charge, but positive. Thus, although an atom can be electrically neutral overall (as is the case with most bulk matter that we are familiar with), it contains negative and positive charges within. It is these charges, and the consequent electric and magnetic forces that they feel, which bind atoms into molecules and bulk matter. We will deal with the forces of Nature in Chapter 7. Here we will focus on these basic electrically charged particles and how they have been used as tools to probe atomic and nuclear structure.
Electron be
ams were being used in the 19th century, though no-one then knew what they were. When electric currents were passed through gases at extremely low pressures, a pencil-thin beam would be seen. Such beams became known as ‘cathode rays’ and, we now know, consist of electrons. The most familiar example of this apparatus is a modern television, where the cathode is the hot filament at the rear from which the beams of electrons emerge and hit the screen.
It was a big surprise in the 19th century when it was discovered that the rays would pass through solid matter almost as if nothing was in their way. This was a paradox: matter that is solid to the touch is transparent on the atomic scale. Phillipp Lenard, who discovered this, remarked that ‘the space occupied by a cubic metre of solid platinum is as empty as the space of stars beyond the earth’. Atoms may be mostly empty space but something defines them, giving mass to things. That there is more than simply space became clear with the work of Ernest Rutherford in the early years of the 20th century. This came about after the discoveries of the electron and of radioactivity, which provided the essential tools with which atomic structure could be exposed.
The electron was discovered and identified as a fundamental constituent of the atomic elements by J. J. Thomson in 1897. Negatively charged, electrons have been inside atoms as long as the Earth has been here. They are easy to extract, temperatures of a few thousand degrees will do. Electric fields will accelerate them, giving them energy and thereby enabling beams of high-energy electrons to probe small-scale structures.
There are other atomic bullets. The proton has positive electric charge, in magnitude the same as the electron’s negative, but in mass the proton wins out immensely, being nearly 2,000 times as massive. Protons have become a choice beam for subatomic investigations, but initially it was another electrically charged entity that proved seminal. This was the alpha particle.
Today we know that this is the nucleus of a helium atom; a compact cluster of two protons and two neutrons, and as such, positively charged and some four times as massive as a single atom of hydrogen. The reason that this came to prominence is that the nuclei of many heavy elements are radioactive, spontaneously emitting alpha particles and thereby providing freely a source of electrically charged probes. Heavy nuclei consist of large numbers of protons and neutrons tightly packed, and the phenomenon of alpha radioactivity occurs as a heavy nucleus gains stability by spontaneously ejecting a tight bunch of two protons and two neutrons. The details of this need not concern us here, suffice to accept that it occurs, that the ‘alpha’ particle emerges with kinetic energy and can smash into the atoms of surrounding material. It was by such means that Ernest Rutherford and his assistants Geiger and Marsden first discovered the existence of the atomic nucleus.
6. Result of heavy and light objects hitting light and heavy targets, respectively.
When alpha particles encountered atoms, the alphas were sometimes scattered violently, even on occasion being turned back in their tracks. This is what would happen if the positive charge of a heavy element, such as gold, is concentrated in a compact central mass. The positively charged alphas were being repelled by the positively charged atomic nucleus; and as a light object, such as a tennis ball, can recoil from a heavy one, such as a football, so did the alphas recoil from the massive nucleus of the gold atom.
Alphas are much lighter than the nuclei of gold but heavier than a proton, the nucleus of the hydrogen atom. So if alpha particles are fired at hydrogen, one would have a situation akin to the football hitting the lightweight tennis ball. In such a case, the football will tend to carry on in its flightpath, knocking the tennis ball forwards in the same general direction. So when the relatively massive alphas hit the protons of hydrogen, it is these protons that are ejected forwards. These were detected by the trails they left in cloud chambers (see Chapter 6).
By such experiments in the early years of the 20th century, the basic idea of the nuclear atom was established. To summarize: the way that the alpha particles scattered from atoms helped to establish the picture of the atom that we have known ever since: the positive charge lives in a compact bulky centre – the atomic nucleus – while the negatives are electrons whirling remotely on the periphery.
Naturally occurring alpha particles don’t pack much punch. They are ejected from heavy nuclei with only a few MeV kinetic energy, or equivalently a few MeV/c momentum, and as such are able to resolve structures on distance scales larger than about 10–12 m. Now, such sizes are smaller than those of atoms, which makes such alphas so useful, but are still much larger than the 10–14 m extent of even a large nucleus, such as that of a gold atom, let alone the 10–15 m size of the individual protons and neutrons that combine to make that nucleus. So although alphas were fine for discovering the existence of the atomic nucleus, to see inside such nuclei would require beams with more energy.
With this as the aim, we have here the beginnings of modern high-energy physics. It was in 1932 that the first accelerator of electrically charged particles was built by Cockroft and Walton, and a detailed picture of nuclear structure, and of the particles that build it, began to emerge. One can use beams of atomic nuclei, but while these were truly ‘atom (or rather nuclear) smashers’, and helped to determine the pattern of nuclear isotopes (forms of the same element that contain equal numbers of protons but different numbers of neutrons) and their details, the clearest information on their basic constituents came with the simplest beams. A nucleus of carbon contains typically six protons and a similar number of neutrons. As such there is a lot of debris when it hits another nucleus, some coming from the carbon beam itself as well as that from the target. This makes a clear interpretation difficult. It is far cleaner to use a beam of just protons; this was, and remains, one of the main ways of probing the nucleus, and distances down to 10–19 m today.
Protons, which carry the positive charge, have been favourites for over 50 years as they pack a big punch. However, electrons have some special advantages and much of our present knowledge about the structure of atomic nuclei, and even the protons and neutrons from which they are made, is the result of experiments using electron beams.
Radioactivity in the form of beta decay emits electrons – the ‘beta’ radiation – which could be used to probe atomic structure. However, such electrons have energies of only a few MeV, as was the case for alpha particles, and so suffer the same limitations: they allow us to see a nucleus like the alpha can, but cannot resolve the inner structure of the nucleus. The key to progress was to ionize atoms, liberating one or more of their electrons, and then accelerate the accumulated electron beam by means of electric fields. By the 1950s in Stanford, California, beams with energies of 100 MeV to 1 GeV per electron began to resolve distances approaching 10–15 m. The electrons scattered from the protons and neutrons began to reveal evidence of a deeper layer of structure within those nuclear particles. Such experiments showed that the neutron, though electrically neutral overall, has magnetic effects and other features suggesting there is charge within it, positive and negative counterbalancing somehow, as had been the case in atoms. Protons too were found to have a finite size, extending over a distance of order 10–15 m. Once it was established that protons are not point particles, the question arose as to how the charge of a proton is distributed within its size. Such questions are reminiscent of what had happened years before in the case of atoms, and the answers came by similar experiments. In the case of the atom, its hard nuclear core was revealed by the scattering of alpha particles; in the case of the proton, it would be beams of high-energy electrons that would give the answer.
It was the 3-km-long linear accelerator of electrons at Stanford that in 1968 took the first clean look inside the atomic nucleus and discovered that what we know as protons and neutrons are actually little spheres of swarming ‘quarks’.
At energies above 10 GeV, electrons can probe distances of 10–16 m, some ten times smaller than the proton as a whole. When they encountered the proton, the electrons were found to be s
cattered violently. This was analogous to what had happened 50 years earlier with the atom; where the violent scattering of relatively low-energy alpha particles had shown that the atom has a hard centre of charge, its nucleus, the unexpected violent scattering of high-energy electron beams showed that a proton’s charge is concentrated on ‘pointlike’ objects – the quarks (pointlike in the sense that we are not able to discern whether they have any substructure of their own). In the best experiments that we can do today, electrons and quarks appear to be the basic constituents of matter in bulk.
Chapter 4
The heart of the matter
* * *
This chapter features up and down quarks, the electron, and the ghostly neutrino – the roles they play and how their masses and other properties are critical for making life, the universe, but not everything; cosmic rays and evidence of extraterrestrial forms of matter that do not occur naturally here on Earth; neutrinos – their production in the Sun and stars, and neutrino astronomy.
