2006-7 Module 113 - Lecture 1

Module 113- Quantum theory and atomic spectroscopy LECTURE 1 – Sub-atomic structure 1. What is an atom? What we know today

We have a very tidy picture of what an atom is based on the work of particle physicists. They have come up with a model that explains virtually all the relevant physics which has the prosaic name the Standard Model. According to the Standard Model, there are twelve fundamental particles. These fundamental particles have a definite mass and charge that does not change with time or environment. Six of these are called quarks, and they are subdivided into three pairs. The other six fundamental particles are called leptons and they are also arranged into three pairs. Each lepton pair contains a neutrino, a very peculiar particle that carries very little mass and can only interact very weakly with atomic matter. Virtually all atomic physics involves just one pair of quarks and one pair of leptons as follows: quarks leptons

u and d e and υe

(sometimes called up and down) the electron and the electron neutrino

This is because these four are stable: the other eight fundamental particles are not and ultimately decay into the four above.

Since the neutrino only interacts weakly with matter, atomic physicists only worry about neutrinos when dealing with radioactive decay so we’ll ignore it from now on. Quarks are gregarious particles: indeed, we never see a quark alone but in groups we call hadrons. A pair of quarks can form a meson, and billions of such particles are formed in the atmosphere every hour by the interaction of cosmic rays with atmospheric molecules. More importantly, three quarks can form a baryon and in atoms we find two types of baryons; protons and neutrons. Both are formed by combinations of up and down quarks. proton neutron

made up of

uud udd

The only problem with the Standard Model is it does not explain why there are twelve fundamental particles, nor why they have the mass and charge they do. That is still to be discovered and physicists are already happily spending millions of pounds of taxpayers’ money trying to work it out. Which is nice.

A key point to realise is that the Standard Model was not plucked from the air but was based on the results of hundreds of experiments that had revealed dozens of wonderful and exotic particles that are not normally stable here on earth but can be created in a laboratory or in deep space. So in answer to the title question an atom is formed from quarks (as neutrons and protons) and electrons.

…but a century ago… Back in 1890, we hadn’t discovered electrons, protons and neutrons and certainly there was no evidence for quarks lying around. The history of our understanding of the nature of matter, or “what stuff is made of” is also an interesting case study in the nature of the scientific method itself. Way, way back (440 CE or thereabouts), the Greeks LEUCIPPUS and DEMOCRITUS had a kind of atomistic model- that the things we see are made up of smaller, indivisible components. This would explain how coastlines eroded and objects graded become old and worn but unfortunately, the great “scientist” Aristotle didn’t like it very much. However, from a modern viewpoint Aristotle wasn’t actually very scientific in his methods. Thanks to Asiatic vandalism by the early medieval period no-one in the West knew anything about Greek science except the work of Aristotle, so the atomic model was forgotten. Indeed, some argue that for about 150 years after the death of Alexander the Great more scientific progress was made than would be achieved in the following 1500 years afterwards. For example, ARISTARCHUS determined that the sun was actually at the centre of the solar system in the 3rd century BCE, but almost all this original work had been lost! Although science went on a bit of a decline during the Roman Empire, it was the rise of Christianity that really finished ancient science off: the finale is often set as 415 CE when the female mathematician HYPATIA was lynched for religious reasons in Alexandria. In the late medieval period, Greek science returned thanks to Islamic scholars (whose chums were smashing up Europe at the time): they also brought chemistry with them thanks to their love of arak or anise. Eventually, thanks to Copernicus and Galileo it was obvious that Aristotelian science was hopelessly wrong about almost everything (like how many elements there were and the Earth being the centre of the Universe), though we must be careful not to equate what the ancient scientists actually understood with what the Renaissance scientists thought they understood. So the debate about whether atoms existed raged on through the Renaissance and into the Enlightenment: but amongst the atomists were some big names like BOYLE and NEWTON. But it was an English chemist John DALTON, who fully developed the idea between 1803 and 1805 that the elements are indeed composed of atoms, and that atoms of the same element were identical and distinct from other elements and used it to explain a number of scientific observations. This meant that there existed as many elements as there were different atoms. He also concluded that molecules like water are composed of these atoms. Unfortunately, a large number of John Dalton’s papers were destroyed when the Luftwaffe bombed Manchester in December 1940.

Unfortunately, he and many others took identical to mean possessing the “same mass”. This was to cause all sorts of problems, and was only really solved when the true structure of atoms was understood in terms of protons (which determine the atomic number or identity of an element) and neutrons (who add additional mass and are responsible for the different isotopes of an element). But that was another 120 years later! We will cover 100 or so years of this period in the first lecture.

Subatomic Structure Still, what gives these atoms for each element their unique chemical and physical properties? No-one could explain this, but questions such as this led to much speculation that atoms were themselves made of smaller particles, in some way because this was logical extension of the whole atomic concept. Early guesses (because this is all they really were) included AMPERE 1814 – atoms contain electrical currents (well, electricity was his favourite subject) Gustave Theodor FECHNER 1828 – “gravity model” (later in life he was a pioneer in the wonderfully named subject of “psychophysics” the branch of psychology concerned with quantitative relations between physical stimuli and their psychological effects: not physics performed by psychotics). The “solar” model was first posited by Thomas Hobbes, the Carolingian philosopher who was also a big mate of Galileo (see a connection here?) Wilhelm Eduard WEBER 1871 – “electrostatic model” (and it will come as no surprise that he was a big name in electrostatics and magnetism) However, none of these people really had any proof or suggested any experiment to discover what the constituents of the atoms really were. Technically, one could argue that they all were on to something, but that is rather like saying because someone picks the correct side of a flipped coin, they have “predicted” the outcomeany fool can be right about the future, at least some of the time.

Discovery of electrons and protons- Cathode Rays No one in the mid-1850s knew of the existence of electrons, protons and neutrons, let alone any of their properties. A technical innovation- the cathode ray tube- invented in 1855 by Heinrich GEISSLER, led to the discovery of two of the crucial constituents, but no one could have predicted that at the time. This is rather a good example of research in one field (electrostatics) have a profound influence in another (chemistry). In fact, it was the development of the mercury vacuum pump by Geissler that allowed the production of the first cathode ray tube because it could extract the air from a glass vessel. Eventually, such pumps would allow the development of the first electric light bulbs. Anyway, a cathode ray tube has two electrodes in a sealed vessel (usually glass) containing a low-pressure gas. A voltage is applied to the electrodes and a current can pass through the gas.

The problem was no-one understood the mechanism responsible for the conduction of electricity through the gas. So scientists began all kinds of experiments to find out just what was happening: Julius PLUCKER 1858- showed that cathode rays bend under the influence of a magnet SPRENGEL 1865 using a phosphor coating, observed a cathode glow, which was affected by a magnetic field Johann Wilhelm HITTORF 1869- cathode rays travel in a straight line which was a well known property of waves like light. Unfortunately, no one could prove he was pretty close till 1928! Cromwell FLEETWOOD VARLEY 1871 – his experiments suggested the cathode rays were more like particles. Philipp LENARD was a big fan of HERTZ (who demonstrated that light was an electromagnetic wave) and appears to have based his entire career on mimicking his hero. On advice from the Great One, he invented the “Lenard window”, a thin foil of aluminium that replaced one of the glass windows of the cathode ray tube. The film was capable of holding a vacuum, but thin enough to allow the cathode rays to escape from the production region to become free rays available for experiments (just think how much more difficult spectroscopy would be if you had to do it INSIDE a light bulb!) Lenard was brilliant experimentalist, but a grumpy old sod, always complaining he was in the shadow of Hertz which was a bit rich (and inevitable) Experiments on free cathode rays revealed two important properties 1. they were CHARGED PARTICLES 2. they were very TINY, much, much smaller than an atom Eugen GOLDSTEIN – discovered canal rays, which have a charge of opposite sign to cathode rays. George Johnstone STONEY (Queen’s University Dublin) 1894 – he coined the term electron for the “atom of electricity” and even determined its charge, which we now call the coulomb. Mind you, the official discovery of the electron is actually taken to be the experiments of Joseph John THOMPSON in 1897, which succeeded in measuring the CHARGE TO MASS RATIO of an electron:

me ~ 10 −7 for cathode rays e Thompson’s result suggested once and for all that electrons must be particles (waves don’t really have a mass). This goes to show you that often a discovery is the result of many, but over time becomes accredited to one. It was also found that for canal rays, the above ratio was 1000 times larger (that is, the canal rays were much heavier) (Today, we know canal rays are protons, otherwise known as the hydrogen ion H+ which has a mass 1836 times that of an electron) Where were these cathode rays coming from? Well, many speculated they were present INSIDE the atoms of the cathode ray tube’s electrodes, and were somehow released when the high voltage was applied. Two further “proofs” were put forward: 1. Radioactivity- α and β rays are released from unstable atoms such as 14C- in 1899, β rays were shown to really be electrons.

2. The Zeeman effect (the splitting of the spectroscopic lines in a magnetic field- more on this later in the course) was explained by LORENTZ as the result of “electron motion” in an atom However, these two proofs were both complete nonsense – β rays come from the decay of the atom’s nucleus (the neutrons decay into protons, electrons and neutrinos) and are not the electrons that are available when we do ordinary chemistry (chemistry is all about swapping electrons around: therefore breaking and forming chemical bonds). Meanwhile the Zeeman effect has nothing to do with the Lorentz theory and it is best not to think it has anything really to do with electron “motion”. Yet the conclusion- electrons are constituents of atomsis correct and is a great example of reaching the right conclusion by the wrong route. This sort of thing gives social scientists a complete field day as they try and claim we are all under some kind of mass hypnosis that makes us believers in electrons and that they are nothing more than figments of our imaginations. The electron hypothesis has been tested countless times since and has never failed: atoms are bags of electrons waiting to do chemistry. An atom is electrically neutral, so these electrons are balanced by positive charges: but how are these positive and negative charges organised in an atom?

The structure of an atom- the Rutherford model

Lenard measured the absorption of electrons by materials as a function of the electron velocity (which could be controlled using an electric field) and realised that electrons were tiny with respect to the total volume of the atom. Now, atoms were electrically neutral, so it seemed logical that the “rest” of the atom was positively charged, and that it was much larger than the volume occupied by the electrons. However, J.J. Thomson (him again) speculated that maybe most of the atom was “empty”- his model envisioned a shell of positive charge surrounding a “gas” of electrons. Again, there wasn’t a great deal of proof for any of these models. The big change came when Hans GEIGER and Ernest MARSDEN (working for Ernest RUTHERFORD) actually performed an experiment to find out: using α particles and some gold foil. Rutherford’s name doesn’t even appear on the original paper reporting the result (“On a diffuse reflection of the particle”, Proc. Roy. Soc. A82, 495 (1909)). The remarkable feature was the huge deflection suffered by a small number of α particles.

Using this result, Rutherford proposed the nucleus model, where all the positive charge is concentrated in the centre of the atoms, surrounded by the “electron gas”. He was rather mean in leaving both his students off this crucial paper that explained the results of the Geiger and Marsden experiment, but then Rutherford understood that often it is not what you did but what people THINK you did that is important- today no one knows who Geiger and Marsden are, but Rutherford has gone down in history as “discovering” the nucleus.

We’ve established that the atom has two components: a compact positive part and a not so compact negative part. But if the negative part contains electrons, how many? Do all elements have the same number of electrons, or does it change? What makes a sulphur atom different from a carbon atom? The answer came from studying the interaction of X-rays with atoms, and this introduces nicely a crucial experimental technique for studying matter: spectroscopy, or the interaction of matter with electromagnetic (E.M.) waves. Before we do, let’s go back to chemistry: were there any clues that Dalton’s mass boo-boo (equating different mass with different elements) was causing problems? Well, the end of the 19th Century brought a couple of problems: the discovery of the first Nobel gas on earth, argon, in the 1890s by Lord Rayleigh and William Ramsay. Argon was an awkward discovery because it didn’t seem to fit in Mendeleev’s periodic table. When the other noble gases were discovered, they were added as a whole new group to the periodic table, which temporarily solved that little dilemma but obviously the periodic table had failed to “predict” the noble gases. The incident does highlight that there were a number of weaknesses with the all-powerful periodic table 1) 2) 3) 4)

Were there elements lighter than hydrogen? How many rare earth elements were there? Were there elements heavier than uranium, the heaviest then known? Why could the elements be arranged in such a table? Why was gallium, say, so like indium?

A further problem came from studies of radioactivity. The radioactive elements decayed into a series of products, but many were radioactive and had different masses to the elements already discovered. By Dalton’s rule, this meant they had to be different elements. Did this mean that we had to fit whole new groups, and even rows, into the periodic table? Fundamentally, the problem with the periodic table was it was just a clever way of organising the elements: no one knew why argon and helium belonged to the same column, or why gallium should be in the same row as bromine. It had the same essential weakness that the standard model has today: it explains what the world is made of but not why the world is like this!

2. Atomic Spectra Electromagnetic waves can travel enormous distances and carry large amounts of energy, so they can affect the environment they travel through and be easily detected. They are an excellent method of remote sensing, the detection of material over large distances. As a result, spectroscopy really began with astronomy and the spectrum of sunlight first recorded by William Hyde WOLLASTON (1802), who appears to have just about dabbled in everything- he even discovered palladium and rhodium. If you disperse starlight with a prism (to separate the different frequency components), you see a series of dark lines superimposed on the continuous spectrum of light. A similar effect was observed in flames (Joseph FRAUNHOFER 1812). Fraunhofer was very canny and published tables of the lines for the optics industry, which used it for quality assurance tests on prisms (yawn), so that we now call them the Fraunhofer lines. We will meet the so-called Fraunhofer-D lines again soon.

David BREWSTER and others suggested that these lines allow us to analyse the luminous environment, that selective absorption or emission of light at a certain wavelength indicates the presence of certain elemental species (spectral analysis). You all know about flame tests- well, obviously sodium seems to be associated with particular wavelengths that are different to, say, potassium.

The most spectacular use for spectral analysis came in 1856 when William SWAN discovered that the dark lines in sunlight matched the same wavelength of those he could make in a lab from a sodium flame and hence discovered that sodium must be present in the sun. In fact, many individual spectral lines could be associated with a particular element. In 1864, William HUGGINS identified the same lines in light from starlight, proving that basically the sun was just another star. Robert Wilhelm BUNSEN and Gustav KIRCHOFF perfected the flame tests and developed the spectroscope, the grand-daddy of all spectrometers today. Using this device, they discovered a number of new elements including caesium, then in 1859 discovered a series of metals in the sun’s spectrum. In 1862, Anders ANGSTROM identified hydrogen as a major component of the sun, and during an eclipse in 1868 Norman LOCKYER saw an unknown emission line which he attributed to an entirely new element- helium (he later founded the journal Nature, wrote on average a scientific paper every 42 days and explained that it is the spin of a golf ball that allows it to travel so far when struck).

As the 19th Century progressed, newer forms of electromagnetic energy were being discovered and harnessed. As scientists learnt to record these different spectral regions of the E.M. spectrum, more and more spectral lines were uncovered. By the beginning of the last century, spectroscopy using X-rays (extremely energetic forms of E.M. waves) were being used to identify elements too. X-rays can either scatter off the electrons in an atom (to give secondary X-rays) or tear them away from the nucleus.

Charles Glover BARKLA (born in Widnes) discovered in 1906 that each element has its own characteristic secondary x-ray spectrum (and so got the Nobel prize in 1917) and in 1911, an interesting trend; if you divided the mass of the atom by that of hydrogen, the result scaled at approximately twice the intensity of the scattering signal. He correctly surmised that the scattering was due to the atomic electrons, and therefore the number of electrons in an atom was proportional to roughly half the atomic mass. This result was welcomed with open arms by those working with the radioactive atoms. After many years and many dodgy explanations, Frederick SODDY (1913) proposed that atoms of the same element could have different masses known as isotopes. Antonious VAN DER BROEK coined the term atomic number to distinguish different elements, rather than just the mass, identifying this as the nuclear charge. Frederich PANETH and Georg VON HEVESY stated that while elements could exist in different isotopes, that have different masses, these isotopes are chemically identical. In 1916, Paneth stated a definition of a chemical element that is recognisable today An element is a substance in which all the atoms have the same nuclear (positive) charge.

Still, this meant that there was a great deal of mass in the nucleus that had no nuclear charge and led to the presence of different isotopes. This led eventually to the discovery of the neutron. However, in 1916 all we have really shown is that an atomic nucleus has a positive charge, equal but opposite to that on its electrons and a mass which seems to be an integer multiple of the nucleus of a hydrogen atom. It is not obvious at this point that it contains quanta of positive charge- protons. Indeed, there is a good argument against this- won’t the electrostatic repulsion between these individual protons blow the nucleus apart? The solution to that would have to wait until a new force- the strong force- was discovered which can overcome the Coulombic repulsion between the protons. Another problem with this simple atomic picture is that if electrons are moving around an atom, then classical electrodynamics tells us that a moving charge will radiate electromagnetic energy. So what you might say but this means by conservation of energy that the electrons will lose kinetic energy and ultimately spiral into the nucleus. Why doesn’t this happen? Obviously, spectra could be used to identify atoms (and later, molecules), and indeed in 1898 the spectrum of radium was recorded many years before Marie CURIE isolated and purified the element. Thankfully, the chemist Alexander MISCHERLICH (at about the same time as a physicist Eleuthere MASCAT) wanted to go even further and asked a more fundamental question; do spectra give us the key to the structure of atoms? What is it about an atom that causes these spectral lines to appear? So we have two mysteries to solve • •

How are the electrons in an atom arranged around the nucleus? If they are moving around the nucleus, why don’t they lose energy and spiral into the nucleus? What do the lines in an atomic spectrum actually signify?

Next lecture, we will solve this little mystery thanks to an old man trying to make a better light bulb (sort of)! Key points in lecture 1 • •

Atoms are composed of electrons and quarks, the latter arranged as protons and neutrons. The structure of the atom was discovered by a series of experiments: the theory lagged behind and was not fully in place till the 1920s.

Below is a modern photograph of the spectrum of sunlight, where you can clearly see hundreds of absorption features, each responding to atoms and even some molecules in the sun’s atmosphere.