The Thomson atom

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.

The Rutherford atom

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.

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).

Isotopes

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.

Table 6.1 Some common elements, their isomer nomenclature and comments

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

* Not occurring at > 1% but listed because of inclusion in discussion above.

Intra-atomic forces

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.

Dictionary Definition

COULOMB’S LAW

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):

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