20 minutes reading time (4000 words)

    The Structure of the Atom

     Introduction

    The previous article in this series looked at the development of the atomic theory of matter. The process began with the ancient Greeks and their thoughts on matter and its composition. Experimental results obtained by many people through the succeeding centuries eventually led to the acceptance of atomic theory. A key point in its acceptance was Dalton's proposition that the laws of definite, multiple and equivalent proportions (which were derived from the results of many experiments) could be explained if all; matter was made up of indivisible particles called atoms, provided that:

    • Every kind of atom has a definite weight.
    • Different elements have atoms differing in weight.
    • Atoms combine (to from compounds) in definite ratios of (usually small) whole numbers.

    The purpose of this article is to trace the interaction of theory and experiment in the further development of our understanding of the structure of matter. The timeline shown in Figure 1 is intended to illustrate this interaction.

    The discovery of sub-atomic particles

    The ideas that form the basis of the atomic theory have stood the test of time since they were crystallised in Dalton's proposition. However, one of the more important modifications of the atomic theory involves the idea that atoms were indivisible. Our modern theory says that atoms are indivisible by chemical means. The reason for this change is that it has proven possible to divide or break up atoms using physical means.

    Applying the scientific method, the statement that atoms are indivisible is a challenge to scientists to find ways of dividing atoms, or evidence for their division. This challenge was taken up by many people. One way of doing this is to try to find particles that combine to make up atoms.

    Electrons and protons

    J.J. Thomson (1856-1940) and Eugene Goldstein (1850-1931) were largely responsible for the discovery of the charged sub-atomic particles, the electron and proton. Both of these scientists made use of a piece of apparatus known as a discharge tube (sometimes called a cathode ray tube, or Crookes tube)that had been used by a number of scientists since about 1860. This is a sealed tube in which an electric current is passed through a gas that is held at reduced pressure inside the tube.

    Interaction of theory and experiment in the further development of our understanding of the structure of matter.
    Putting a high voltage between two electrodes results in one of them, the anode, becoming highly positively charged, while the cathode becomes highly negatively charged. The only way that these charges can be reduced is for charged particles to move from one electrode to the other through the gas, and when they do so they create a glow due to interactions with the remaining gas in the tube. Most of the glow is due to particles moving from the cathode to the anode, and this beam of particles was called a 'cathode ray'.

    In 1886, Goldstein used a discharge tube with a hole in the cathode. When he did this he observed that there was a faint glow beyond the cathode as well as the glow between the electrodes. He concluded that since the charged particles that must have caused this glow were moving towards and past the cathode, they must be positively charged. He called these rays 'canal rays'.

    In 1897, J.J. Thomson used a discharge tube around which he had positioned electrodes and a magnet so that he could investigate the charge and mass of the particles making up the cathode ray. By comparing the deflection of the particles caused by known electric and magnetic fields, Thomson was able to determine the mass-to-charge ratio of the particles. He found the same ratio, no matter what type or combination of electrodes and gas he used in the discharge tube. Therefore the particles were unlikely to be ions of the materials/elements that were used in the experiment, and he concluded that these particles must be present in all types of atom. That is, that they must be sub-atomic particles. These particles were later called electrons.

    Soon after, scientists performed similar experiments on Goldstein's canal rays. They found that the mass-to-charge ratio of these particles varied with the gas that was in the tube. The smallest ratio was obtained when hydrogen was used, and they found that, if they assumed the same charge for all the particles, all the larger particles had masses that were multiples of the hydrogen particle. It was suggested that these positively charged particles were atoms that had given up an electron to the anode become positively charged, and therefore moved towards the cathode. Further, they proposed that the positive ion from the hydrogen atom was a fundamental particle that formed part of all atoms. The proton, as this particle is now called has a mass- to-charge ratio approximately 1836 times larger than that of the electron, and atoms can be distinguished by the different number of protons (and electrons) that they possess.

    Isotopes

    An interesting complication was revealed by Frederick Soddy (1877-1956) and T.W. Richards (1868-1928) when they independently demonstrated that the lead that results from the radioactive decay of uranium 238 has an atomic weight of 206, while that from decay of thorium 232 has a weight of 208. Soddy differentiated between these two types of lead by calling them different isotopes. These atomic weight determinations were made using very tedious chemical techniques.
    Thomson continued his experiments with the discharge tubes filled with chemically pure samples of gases, and in 1912 he found that certain of these gases gave more than one value of charge to mass for the positive ions in the canal rays. In particular, he found that neon, which has an atomic mass of 20.18, gave two different charge-to- mass ratios. His conclusion was that there must be more than one type of neon atom. One of Thomson's students, Francis Aston (1877-1945), succeeded in separating these two types of neon using their different rates of diffusion through a porous plug between two containers. The different atomic masses that were determined for each of these samples showed that there must be more than one type of neon. In 1919 Aston built the first of many mass spectrometers and, since this technique allowed mass-to-charge ratios of ions (and hence masses of atoms) to be easily determined, he subsequently showed that many elements have isotopes. This naturally lead to the possibility that not all of the sub-atomic particles had been discovered as there had to be a reason for the existence of isotopes.

    Neutrons

    The neutron is an uncharged particle with a mass similar to (but slightly larger than) that of a proton. It was first proposed to exist by Ernest Rutherford (1971-1937) in 1920, and the proposed mass would account nicely for the mass data obtained from experiments like those described above and for the existence of isotopes (which have different numbers of neutrons). In 1932, James Chadwick (1991 -1974) bombarded a sample of beryllium with alpha particles (nuclei from helium atoms), and observed a beam of rays being given off. Experiments with electric and magnetic fields showed that the particle was electrically neutral, and the mass was eventually shown to be similar to that of a proton (approximately 1839 times that of an electron), the different weights of the isotopes mentioned in the previous section can therefore be explained by proposing the presence of different numbers of neutrons in the nuclei.

    Early atomic models

    Once scientists had shown that atoms were built from a number of other particles, a new question becomes important. That is, how are these particles put together? Prior to the discovery of the electron, atoms were thought to be extremely small spheres (Dalton's model, or theory of atomic structure, in which the atoms are like billiard balls), or various types of polyhedra (the models of Plato and Aristotle). New ideas were needed to deal with the question of the construction of atoms, since the 'shape' of an atom would depend on the way it was put together, and would affect the ways in which atoms could combine with one another.
    When Thomson discovered electrons, he simply incorporated them into Dalton's theory (which envisaged atoms as being solid spheres, rather like billiard balls). He therefore modified the theory by proposing that atoms were spheres which had these small negatively charged particles distributed throughout them, rather like plums in a pudding. Since he knew that atoms were electrically neutral, he proposed that the rest of the sphere was positively charged, and that the atoms were packed together like balls in a box.

    With a theory in front of them scientists had something to test. In 1911, Rutherford devised an experiment to test the 'plum-pudding' model of the atom. He and his students, Geiger and Marsden, fired a beam of alpha particles at a thin piece of metal foil (gold, silver and copper were used). As with any experiment, a prediction should be made on the basis of the accepted theory and the results compared with the prediction. According to the Thomson model of the atom, the positively charged balls are packed closely together, so that the alpha particles cannot pass between the gold atoms. The size of the gold atoms would mean that the positive charge is only spread thinly through the sphere. This low charge density would mean that the repulsive force between the positively charged alpha particles and the gold atoms would be insufficient to stop or repel the alpha particles, but that they could be deviated slightly. Also, since the mass of each of the electrons in the gold atom is so much less than that of an alpha particle (>7400 time less), they cannot cause the alpha particles to deviate much either (due to an argument based on the relative momenta of the particles). It would therefore be predicted, on the basis of the Thomson model, that all of the alpha particles would pass through the foil (and through the gold atoms), and that the deviation of the particles should only be small.

    The result from the experiment was that a large number of the particles passed right through the foil, some were deviated, sometimes by quite large angles and, surprisingly about 1 in 10,000 were bounced back. It would have been tempting to dismiss the small number that bounced back as being due to experimental error, but it was reproducible, and had no obvious cause. It was time to consider modifying or changing the theory to account for such large deflections.

    The deviations and the bouncing back must be due to repulsion of the alpha particles by something with a much higher positive charge density than proposed for an atom by Thompson's model. Simple electrostatic calculations (using Gauss' Law) show that diffuse spheres of positive charge cannot cause such large deviations. Indeed, Rutherford was able to show, using such calculations, that his results were only consistent with the positive charge being held on particles that are no larger than 10-14m in diameter. This result lead him to propose the nuclear model of the atom. In this model, most of the mass is in the nucleus, along with the positive charge, and the light, negatively charged electrons orbit around the nucleus, like planets around the sun.

    The Bohr model of the atom

    Rutherford's nuclear model of the atom was a major advance, but it had several flaws:

    1. The application of the laws of classical, Newtonian physics would require that electrons, like any charged particle, moving in such circular paths should continuously emit radiation. No such radiation was observed.
    2. Charged particles moving around a nucleus should give off energy (as the radiation mentioned in 1), which should lead to the electrons spiraling in towards the nucleus due to electrostatic attraction (according to principles of conservation of energy). This would result in the collapse of all matter, which is clearly not the case.
    3. It had been known for some time that each element will absorb and emit particular energies of light (the discovery of a material with new emission lines was considered compelling evidence for the presence of a new element). Rutherford's nuclear theory failed to explain the origin of these (emission and absorption) spectra.


    Niels Bohr (1885-1962) deduced that, since atoms did not collapse and did not give off energy, classical physics could not be used to explain the motion of electrons in atoms. He went further and said that the electrons circled the nucleus without loss of energy, and that they could only move in circular orbits of certain energies. This last point is called quantisation, and could be used to neatly explain the emission lines that are characteristic of elements. The Bohr model of the atom proposed that the first orbit could contain two electrons, the second, eight, and so on. That is, the number of electrons in the nth orbit is equal to 2n2.


    In the simple case of the hydrogen atom, where there is only a single electron, Bohr was able to calculate the energies of the radiation to be expected from electrons moving between these orbits. He was even able to predict correctly an emission line that had not previously been observed. Unfortunately, the presence of extra electrons in larger atoms makes the system too complicated for such a straight-forward approach, and similar calculations of emission wavelengths for larger atoms do not produce the experimentally observed values. Clearly the model had to be refined further in order to describe atoms heavier than hydrogen.

    Another unsatisfactory aspect of this model was the arbitrary way in which the restrictions on the motion of the electron(s) were introduced. There was no explanation given as to why the quantisation occurred.

    The Schrödinger model of the atom

    Albert Einstein (1879-1955) proposed that light could be considered both as waves and as a stream of particles called photons. This proposal was made in order to account for the fact that light gives diffraction patterns when passed through holes that are approximately a wavelength apart (a wave phenomenon) and to account for the photoelectric effect (a particle phenomenon in which photons knock an electron off a surface). In 1924, Louis de Broglie (1892-1987) generalised this idea and proposed that any moving particle could be considered as a 'matter wave', with a wavelength that inversely related to the mass and velocity. Erwin Schrödinger (1887- 1961) then took this idea and, in 1926, proposed that electrons behaved as waves around the nucleus, essentially because they move so rapidly. This means that the electron is smudged out as a complex 3-dimensional wave, all around the nucleus, rather than being at any one point. Quantisation of the type introduced by Bohr is that readily explained as being a result of interference (a property exhibited by waves).

    It turns out (from some rather complex mathematics in a field called quantum mechanics) that this 'wave-particle duality' means that we can only talk of the probability of finding an electron within a certain region of space. That is, this theory is a modification of the Bohr theory of the atom in which electrons are not so much restricted to a certain radius from the nucleus, but rather they are restricted to certain regions of space.

    The regions of space to which the electrons are restricted are called orbitals (retaining the classical nomenclature), each of which can hold up to two electrons. This limitation on the number of electrons that can fit into an orbital is known as the Pauli Exclusion Principle and has its basis in the statistics of quantised systems. Orbitals which have the same energy combine to make spherical subshells and, in turn, subshells of roughly similar radius combine further to give shells of electron density around the nucleus. These shells can be thought of as being roughly equivalent to the allowed radii in the Bohr model of the atom.

    Pictorial representations of some of the orbital shapes are shown in Figure 2. The first shell is small. It contains only one subshell, which in turn contains only one orbital (1s), and therefore has room for only two electrons. The second shell is larger, exists at a larger radius, and contains two subshells (2s and 2p). The first of these subshells has one orbital and the second has three orbitals, so that the second shell can hold a total of eight electrons. The third shell holds three subshells (3s,3p and 3d), nine orbitals and eighteen electrons. These are the same numbers of electrons that can fit into the orbits in the Bohr model of the atom. A great deal of spectroscopic and other experimental data has been obtained and the results are entirely consistent with the predictions from quantum mechanics.

    Orbital shapes for s (spherical) and p (dumbbell) orbitals. d and f orbitals have more complex shapes and can be found in many undergraduate texts.

     All atoms have all of these orbitals (and more), so we have to consider which orbitals are occupied by the limited number of electrons. The nucleus and electrons carry opposite charges, so we would expect the smaller, inner shells to be filled first. However, since the electrons all carry the same charge and therefore repel one another, it becomes more difficult to put electrons into a shell, subshell or orbital that already contains a number of electrons. This has two effects.

    1. If there exists more than one orbital of the same energy, one electron will go in each orbital until they all have one, and then a second electron will go in each. This is known as Hund's Rule. For example, for three p orbitals of a subshell, the first three electrons are placed so that there is one in each of the orbitals. The next three electrons fill each of the orbitals in turn to complete the subshell.
    2. By the time the s and p subshells have been filled in the third shell, there are already a large number of electrons in that region of space. This means that it is quite a bit more difficult to put an electron into the d subshell. In fact, it is slightly easier to put an electron into the 4s subshell than it is to put one into the 3d, which substantially affects the order of filling. In general terms, the order of filling is as follows:
    1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, .......

    This method of building up the electronic configuration of atoms by starting with the lowest energy orbitals is called the Aufbau Principle. The diagram below is a useful way in which to remember this order.

    Joining the arrows head to tail (beginning with arrow a then arrow b and so on) gives the filling order written above. The electronic configuration derived in this way is what is called the 'ground state' electronic configuration. This means that the atom will have the lowest energy possible when it is in this state. An electronic configuration in which have a higher energy orbital is filled at the expense of a lower one is known as an 'excited state'. An atom in an excited state possesses more energy than an atom in its ground state. Returning to the ground state releases the extra energy in the form of a photon of a particular wavelength, giving light in one of the emission lines of that element.

    Order in which orbitals are arranged by increasing energy.

    Overview of atomic structure

    This article has traced the development of ideas about atomic structure. While the steps in this evolutionary process are interesting and important in themselves, it is also important to have a clear idea of what the final outcome is. A clear understanding of the nature of the atom is crucial to any serious study of chemistry. This section collects together some of the more important ideas about atomic structure that have come from centuries of work by chemists, physicists and mathematicians.

    All structures and materials that we use or come across in everyday life are made up of mixtures of chemical compounds, which can be separated from one another by physical means. Chemical compounds are, in turn, made up of atoms that are bonded to one another. These compounds differ from one another in the nature, number and arrangement of their constituent atoms. Atoms in a compound can only be separated by chemical means and, when this is done, new compounds are produced. it follows from this that atoms, and the way they are put together, are responsible, directly or indirectly, for the differences in the properties that we observe for a variety of materials. An atom can be defined as the smallest particle of an element that can enter into a chemical combination.

    All atoms are believed to be made up of a positively charged nucleus surrounded by electrons. Each electron carries a negative charge of 1.6 x 10-19 coulomb and moves around the nucleus in a wavelike manner. In an atom, the negative charges on the electrons balance out the charge on the nucleus. If there are more or less electrons than are required to balance the nuclear charge, the resulting species is called an ion. An ion can therefore be made by adding or removing one or more electrons to or from an atom.

    The nucleus of an atom is much heavier than the electrons that surround it, but most of the volume of the atom is used by the electrons as they orbit the nucleus. The diameter of the nucleus is believed to be between 10-15 and 10-16 metres, while the atomic size is ~ 105 times larger at several ångströms (1 ångström = 10-10 metres). The electrons are believed to arrange themselves in spherical shells around the nucleus. Each successive shell gets larger, a bit like the layers in an onion, and therefore has room for more electrons (the first shell can hold two electrons; the second, eight; the third, 18; the fourth,32, and so on). Each shell is made up of spherical subshells, which are in turn made up of differently shaped orbitals. Each orbital can hold two electrons, and the wave-like properties of the electrons result in them being smudged out, or delocalised, over the whole orbital. An s subshell contains one spherical orbital, and can hold two electrons; p subshells contain three dumb-bell- shaped orbitals and six electrons; d subshells, five orbitals and 10 electrons, and so on.

    The nucleus of a particular element contains a certain number of protons (equal to the atomic number) and one of often several different numbers of neutrons. Atoms with different numbers of neutrons are called isotopes. All atoms with the same atomic number (i.e. the same number of protons and electrons) are said to be of the same element, and they behave the same chemically.

    A sample of an element is made up only of atoms, which all possess the same atomic number. It may be (and often is) a mixture of isotopes, and it may take several forms depending on the ways in which the atoms of the element are linked to one another by chemical bonds. These different elemental forms are called allotropes. The best known example of allotropy is probably that of carbon, which exists as diamond and graphite, and now the ball-shaped fullerenes, but many other elements also have allotropic forms.

    The mass that appears in the Periodic Table for each element is a weighted mean of the isotopic masses. For example, a natural sample of lithium will contain approximately 92.5% of atoms with a mass of 7.016 atomic mass units, and 7.5% of atoms with a mass of 6.015 atomic mass units. The average mass for lithium atoms will therefore be:

    09.25 x 7.016 + 0.075 x 6.015 = 6.941

    A proton carries a positive charge that can balance the charge on one electron (i.e. 1.6 x 10-19 coulomb), while the neutron is electrically neutral (from where it gets its name). Protons and neutrons are approximately 1840 times heavier than an electron, which is why most of the mass of an atom is in the nucleus. 

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