Chapter Six Atomic structure
Figure 6.1 • The periodic table B showing the major elements that occur in the body and their relative contribution to body mass A. Note the chemicals with similar properties occur (for example, F, Cl, Br, I, At or Cu, Ag, Au) in the same column.
Reproduced from Thibodeau and Patton 2006 with permission from Elsevier.
It is important to realize at the outset that the descriptions of atoms and atomic particles that you will encounter here and in other texts are merely models designed to help us understand how atoms behave and interact. As with any model, there is a degree of simplification – in the case of atomic modelling, this simplification is often so gross that the model bears no relationship to reality. Atoms are, pretty much, incomprehensible things: you can’t see them, even with the most powerful microscopes (you will learn why in Chapter 8); you can’t taste them, feel them, hear them; you can’t touch them, merely the fields that surround them.
All that we know about atoms is inferred from indirect experimental observation or mathematical models. At the atomic level, we sometimes have to leave common sense behind and deal with concepts such as particles being in two places at the same time, particles behaving as waves and waves behaving as particles. This is why we have models; there are times when too much knowledge simply confuses the picture. You often don’t need to think of an electron as a three-dimensional, standing probability wave (thankfully) and it is much easier – and more useful – to picture a billiard ball whizzing about and bumping into other billiard balls … just so long as you always remember that electrons aren’t actually billiard balls.
It is somewhat ironic that one of the founders of nuclear physics, J.J. Thomson, was awarded the Nobel Prize for physics in 1906 for discovering there were particles called electrons. His son, George, became the only son of a Nobel Laureate to also win a Nobel Prize when, in 1937, he proved that electrons were (also) waves.
For centuries, man struggled to understand how matter was constructed, whether from discrete, uniform particles in differing proportions or from mixtures of fundamental ‘elements’: earth, water, fire and air. By the 19th century, as we have already seen, science was becoming a respectable, disciplined field and its practitioners had begun to understand the difference between certain types of substances. Most importantly, they discovered that mixtures, such as air, could be separated into their constituent parts whilst compounds were chemically combined and, by using chemistry, could be broken down into other, simpler substances. However, beyond a certain point, it was no longer possible to chemically decompose a substance and these fundamental substances were known as elements.
Therefore, for example, air is composed of a mixture of gases, which are not chemically combined. One of these gases is carbon dioxide, a compound whose molecule consists of two elements, carbon and oxygen. It was generally accepted that these elements consisted of what was then considered a fundamental particle, the atom, and that the atoms for each element must somehow be uniquely different … but how?
With J.J. Thomson’s 1898 discovery of electrons, and the realization that all atoms contained these particles, scientists had their first insight into the structure of the atoms. They knew that atoms were electrically neutral; therefore, there must be a positive charge balancing the negative charge of the electrons. This led to the ‘Thomson’ model of the atoms – also called the ‘plum-pudding’ model. In this scenario, the spherical atom of positively charged matter has electrons studded into it, like raisins in a plum, or Christmas, pudding (Fig. 6.2).
Figure 6.2 • The development of atomic theories. (A) The Thomson or ‘plum pudding’ model in which electrons are embedded in a diffuse, positively charged matrix. (B) The Rutherford model: electrons are orbiting separately around a small, dense positively charged nucleus (in defiance of classical electrostatic theory). (C) The Bohr model of the atom. Electrons orbit at intervals that support standing waves that are integral multiples of their de Broglie wavelength. Each shell consists of a number of sub-orbitals (s, p, d, f etc.), each of which has a discrete energy value associated with it. This model, which utilizes quantum mechanics rather than classical physical theory, is widely accepted and utilized today.
Thomson’s proposal fitted the bill nicely for 13 years until a minor experiment by a couple of (then) minor scientists showed it to be impossible and, in doing so, for ever upset the laws of classical physics. It was an experiment that almost never happened. Hans Geiger was a visiting research fellow working under the direction of the God-like Ernest Rutherford at the University of Manchester.
Geiger’s work on atomic theory is largely forgotten: credit is almost invariably ascribed to Rutherford or, occasionally and more appropriately, to Marsden. Instead, Geiger ended up with eponymous immortality by having a radiation detector named after him, despite the fact that the actual work was done by Müller, after whom the more correctly and completely termed Geiger-Müller counter is also named, though is now almost always shortened, rather unfairly, to ‘Geiger counter’.
For some time, it had been known that α-particles could be slightly deflected when fired at thin sheets of metal foil. This was entirely consistent with the Thomson model of the electron with weak electric forces being exerted on the passing α-particles by the uniformly distributed charges of the ‘plum pudding’ atoms.
To measure for large deflections was a ridiculous waste of time, there was no way in which a thin piece of gold foil could deflect relatively heavy α-particles; it was ‘make-work’ for Ernest Marsden, a rather unpromising PhD student.
To everyone’s surprise, and no little incredulity, Marsden found large deviations. Geiger flatly refused to believe his results and, when he was finally convinced, Rutherford – after whom the experiment is usually named – refused to believe Geiger. When Marsden was sent back to repeat the experiment yet again, he had the idea of placing the detectors on the ‘wrong’ side of the metal foil. He found that, not only were α-particles being deflected through large angles, but some were even being scattered in a backward direction.
Rutherford described this as ‘the equivalent of firing a 15″ artillery shell at a piece of tissue paper and watching the shell bounce back at you’. He sent Marsden back to repeat the experiment once more, this time supervising it himself. Marsden got his PhD with what must still be the most important postgraduate thesis of all time. Sadly, Marsden, like 7 million other young men of his generation, was killed in World War 1 and history was never able to judge whether he was a genius or merely serendipitous. Rutherford’s great contribution was to deduce, correctly, how such a thing could have happened.
He realized that the only model that could account for the α-particles’ extraordinary behaviour was if the positive charge was all concentrated into a small, tightly bound, dense nucleus with the electrons more diffusely dispersed at a distance (Fig. 6.2). This alone could account for the findings: it would mean that much of apparently solid objects was empty space, which was why most of the α-particles passed through the foil without deviation. The light, widely separated electrons had little influence on the passage of the incoming particles but if they came within the electric field of the large, positive charge of the nucleus, they could be deflected or even repelled (Fig. 6.3). In fact, it transpires that 99.999999% of matter is empty space; if the nucleus of a hydrogen atom is represented by a thumb-tack stuck in the middle of a football field, then the electron would be lurking somewhere in the furthest, uppermost row of seats in the surrounding stadium. In Rutherford’s model, the electric field intensity of the gold atomic nucleus is 100 000 000 times that of the Thomson model.
Figure 6.3 • Marsden’s classical experiment in which α-particles were fired at a thin gold foil. Although most α-particles travelled straight through the foil without being altered in their path (A), many showed significant deviation (B, C) or even reflection (D, E) in a manner that was inconsistent with the then prevalent Thomson model of the atom. It was this experiment and its unexpected results that led Rutherford to develop a new atomic model in which electrons orbited a positively charged nucleus.
Geiger and Marsden went on to show that foils of different metals would deflect α-particles in differing amounts and that, from this, they could estimate the nuclear charge, which always turned out to be an exact multiple of the charge of an electron (e), though positive rather than negative (+e). For gold foil, they found that the nuclear charge was +79e. As this charge was unique for each material, elements became defined by the number of protons in their nucleus, the atomic number (Z).
It quickly became apparent that a proton and a hydrogen ion were identical and that the majority of the atom’s mass (99.9995%) resided in the nucleus. There were, however, two problems with Rutherford’s proposed nuclear model. The first was that it didn’t account for isotopes. Isotopes are differing forms of an element; they have the same chemical properties but the mass of their atomic nuclei varies. For example, hydrogen has three isotopes, the common variety that we have just discussed with an atomic mass of approximately one proton; deuterium, which accounts for approximately 0.015% of all hydrogen and has an atomic mass equivalent to two protons; and the much rarer (1:10−15) tritium, which has a third ‘proton-mass’ (Fig. 6.4). The isotopes all have the same chemical properties – you can make H2O using deuterium or tritium; this is so-called ‘heavy water’– but different atomic mass numbers (A), 1 for hydrogen, 2 for deuterium and 3 for tritium.
Figure 6.4 • Different forms of the element hydrogen (H). The figures to the left of the element’s abbreviated form represent the mass number (superiorly), equivalent to the combined number of protons and neutrons in the nucleus (nucleon count), and the atomic number (proton count). The latter is unique to each element, hence it is the same for each isotope of hydrogen shown here. The mass number rises as the nucleon count increases. Hydrogen in its commonest form, 1H, consists of a single proton (A); deuterium 2H has an additional neutron (C) while the much rarer tritium 3H nucleus comprises a proton and two neutrons (D). If the atom loses an electron(s) (or gains one or more), it is no longer electro-neutral and becomes an ion (B).
Perhaps the isotope that has the greatest public awareness is carbon-14. Carbon, which has six protons (Z = 6), normally has an atomic mass number of 12; however, it also exists in a form where A = 14. Conveniently, this form is radioactive and decays slowly back into carbon-12. By finding the ratio of carbon-12 to carbon-14, scientists are able to calculate the approximate age of organic materials, all of which contain large numbers of carbon atoms.
It is also the carbon atom that forms the basis for the definition of the mole, which, as we learned in Chapter 1, is one of the seven fundamental SI units (Table 1.1). You may recall that the mole was defined as the amount of a given substance that contains as many elementary entities as there are atoms in 0.012 kilogram of carbon-12.
One mole of carbon-12 contains 6.022 52 × 1023 carbon atoms, a number known as Avogadro’s constant, in honour of Amedeo Avogadro, an Italian mathematical physicist who demonstrated that, at constant temperature and pressure, identical volumes of different gases contain the same number of particles.
A mole of any substance – be it composed of atoms, molecules, ions, electrons, photons etc. – also contains this number of entities. However, the mass of 6.022 52 × 1023 carbon atoms does not equal 12 g exactly. This is because the sample will not consist of purely ‘12A-carbon’; two other isotopes of carbon also exist. We have already mentioned ‘14A-carbon’, which is radioactive and so will ultimately decay back into a stable isotope but there is also ‘13A-carbon’, which comprises 1.1% of all naturally occurring carbon. So the mass of 6.022 52 × 1023 carbon atoms is actually 12.011 g. This is known as the atomic weight of carbon.
In the 1870s, Dmitri Mendeleev, a Russian chemist, found that, if he arranged chemical elements in order of increasing atomic weight, certain elements with similar properties – for example fluorine, chlorine, iodine and bromine – occurred periodically at regular and predictable intervals. He also spotted that there were obvious gaps in the table and was able to make predictions as to the chemical properties of the missing elements. As his predictions came to be realized, the Periodic Table (Fig. 6.1) became a standard reference tool for all scientists.
Meanwhile, the solution to Rutherford’s isotope problem came with the proposal of the neutron, an uncharged nuclear particle that can be regarded as a combined proton and electron. Thus, the neutron contributes to the atomic mass number but has no influence on the atomic number, which is a function of the proton count only. An element (X) can, therefore, be written in terms of its proton (Z) and nucleon (A) count, with, if appropriate, its ionic charge:
The three isotopes of carbon we discussed become (six protons and six neutrons), (six protons and seven neutrons) and (six protons and eight neutrons). Examples of some of the elements that we have discussed, and others that you are likely to commonly encounter, are given in Table 6.1.
|Element (Z)||Nomenclature of common (>1%), natural isotopes||Comment|
|Hydrogen (1)||, (protinium), (deuterium)*, (tritium)*||Ubiquitous in animal tissue, the element that facilitates magnetic resonance imaging|
|Helium (2)||Nucleus is an α-particle|
|Carbon (6)||*||Carbon dating (see above). The backbone of organic molecules|
|Nitrogen (7)||Main component of air. Component of all proteins and DNA|
|Oxygen (8)||Essential for cellular respiration|
|Sodium (11)||Na+ ion is essential in cell membrane transport|
|Magnesium (12)||Catalyst for enzyme reactions in carbohydrate metabolism|
|Aluminium (13)||Used for X-ray filters and step-wedges|
|Chlorine (17)||Cl− ion is essential in cell membrane transport|
|Potassium (19)||Man-made isotopes used in medicine|
|Calcium (20)||Major component of bones and teeth; Ca2+ triggers muscle contraction|
|Iron (26)||Critical component of haemoglobin|
|Cobalt (27)||Man-made isotopes used in medicine|
|Copper (29)||Key enzymatic component. Used for X-ray filters and anodes/targets|
|Zinc (30)||Key enzymatic component|
|Tin (50)||Used for X-ray filters|
|Iodine (53)||Component of thyroid hormone. Radioactive, synthesized used investigatively and therapeutically|
|Barium (56)||Radio-opaque medium used in radiographic examination of the gastrointestinal tract|
|Gadolinium (64)||Commonest contrast agent for musculoskeletal MRI|
|Tungsten (74)||X-ray machine filament|
|Gold (79)||Used in treatment of rheumatoid arthritis. Was the original foil used by Geiger and Marsden|
|Mercury (80)||Used in traditional thermometers|
|Lead (82)||Used for X-ray and other radiation shielding|
|Radon (86)||Synthetic isotopes used in radiotherapy|
|Radium (88)||Synthetic isotopes used in radiotherapy|
Returning again to Rutherford’s model, there was, as has been already intimated, a second problem. Today, we are so accepting of this basic model of the atom that we are seemingly blind to this fundamental flaw. According to the laws of classical physics – and these were the only physical laws there were in 1909 – Rutherford’s atom should, of course, instantly fly apart. The compressed positive forces of the nuclear protons would, as like charges, repel. This process would be aided by the attraction to the oppositely charged orbiting electrons – assuming a way could be found to limit the mutual repulsion of the electrons themselves.
Electrostatically, Rutherford’s atom makes no sense at all; even if it did, Newton’s laws of motion and Coulomb’s law of electric force would preclude an electron from being able to maintain a stable orbit in the way that the planets travel around the mutually attractive sun – instead it would rapidly spiral inwards and collide with the nucleus.
Coulomb’s law of electrostatic force states that the size of the attraction or repulsion is directly proportional to the size of the charges (Q1 and Q2) and obeys the inverse square law with regard to separation (r):