Atomic Structure

The idea that matter is made of tiny particles is very old. In India, the sage Kanada (Vaisheshika school, about 6th century BCE) spoke of indivisible particles called paramanu, and the Greek thinkers Leucippus and Democritus (about 400 BCE) used the word atomos, 'that which cannot be cut'. But these were philosophies. Chemistry began to count and weigh. Antoine Lavoisier (1774) showed that mass is conserved in a reaction, Joseph Proust (1799) showed that a compound always has the same composition, and in 1803 John Dalton put these facts together into his atomic theory, which he published in 1808.

Dalton's postulates (1808). (1) All matter is made of extremely small particles called atoms, which take part in chemical reactions. (2) Atoms are indivisible and can neither be created nor destroyed in a chemical reaction. (3) All atoms of a given element are identical in mass and properties. (4) Atoms of different elements differ in mass and properties. (5) Atoms combine in simple whole-number ratios to form compound atoms (what we now call molecules). (6) A chemical reaction is only a rearrangement of atoms. See how the laws follow: postulate (2) and (6) explain conservation of mass; postulates (3) and (5) explain constant and multiple proportions.

Atoms, molecules and masses. An atom is the smallest particle of an element that takes part in a chemical reaction; its size is of the order of 10⁻¹⁰ m (1 angstrom, 0.1 nm). A molecule is the smallest particle of an element or compound that can exist independently and shows its properties. The number of atoms in a molecule is its atomicity: helium, neon and argon are monoatomic; hydrogen, nitrogen, oxygen, fluorine, chlorine, bromine and iodine (H₂, N₂, O₂, F₂, Cl₂, Br₂, I₂) are diatomic; ozone (O₃) is triatomic; phosphorus (P₄) is tetra-atomic; sulphur (S₈) is poly-atomic. Atoms are far too light to weigh in grams, so we use the atomic mass unit (u): 1 u is one-twelfth of the mass of one carbon-12 atom (about 1.66 × 10⁻²⁷ kg). This carbon-12 standard was adopted by IUPAC in 1961; before that, hydrogen and later oxygen-16 were used. Atomic masses: H = 1 u, C = 12, N = 14, O = 16, Na = 23, Mg = 24, Al = 27, S = 32, Cl = 35.5, K = 39, Ca = 40. Molecular mass is the sum of the atomic masses: H₂O = 18 u, CO₂ = 44 u, NH₃ = 17 u, glucose C₆H₁₂O₆ = 180 u (a glucose molecule has 24 atoms).

Dalton called the atom indivisible, but by the end of the 19th century experiments with electricity passed through gases showed that atoms must contain smaller, charged pieces. When a high voltage is applied across two electrodes in a glass tube with gas at very low pressure (a discharge tube), glowing rays appear. Studying these rays gave us the electron and the proton; the neutron needed a different experiment later.

Thomson and the electron. Thomson passed electricity through a gas at low pressure and found that the rays from the cathode bent towards the positive plate in an electric field. So the rays carried negative charge. The rays were the same whatever gas or cathode metal was used, so he concluded that the particle is a universal part of all matter. He measured its charge-to-mass ratio, and the name 'electron' had been suggested earlier by G. J. Stoney (1891). A few years later, Millikan (1909) balanced tiny charged oil drops between two plates and showed that every charge is a whole-number multiple of 1.6 × 10⁻¹⁹ C, which fixed the electron's charge and then its mass.

Chadwick and the neutron. Rutherford had guessed that the nucleus must hold something heavy but uncharged, because the nuclear mass was about twice what the protons alone could explain. In 1932 James Chadwick bombarded beryllium with alpha particles and found a penetrating radiation that carried no charge but had a mass nearly equal to a proton's. He had found the neutron, and received the Nobel Prize in Physics in 1935. Because it is neutral, it is not pushed away by the nucleus and is a very good projectile for splitting heavy nuclei; this is why neutrons drive nuclear fission. Remember that the simplest hydrogen atom (protium) has one proton and no neutron. Protons and neutrons are together called nucleons; each is itself made of smaller particles called quarks (a proton has two 'up' and one 'down' quark; a neutron has one 'up' and two 'down').

Why is an atom neutral? The number of protons (+) equals the number of electrons (−), so the charges cancel. If an atom gains electrons it becomes a negative ion (anion); if it loses them it becomes a positive ion (cation). Only electrons move in these changes; the nucleus stays the same.

Once the electron was found, a new puzzle appeared: if the atom is neutral and electrons are negative, where is the positive charge and how is everything arranged? Each model below was an attempt to answer this, and each was replaced when an experiment did not fit it. Learn them as a chain: every model fixes the failure of the one before it.

Thomson's model (1904). The atom is a positively charged sphere with the negative electrons embedded in it, like seeds in a watermelon or plums in a pudding; the total positive charge equals the total negative charge, so the atom is neutral. It explained neutrality and the existence of electrons, but it could not explain how alpha particles behaved when fired at a thin metal foil.

Rutherford's gold-foil experiment. Hans Geiger and Ernest Marsden, working under Ernest Rutherford (1909), fired fast alpha particles (helium nuclei, positively charged) at a very thin sheet of gold foil. Gold was chosen because it is so malleable that it can be hammered into an extremely thin foil, only a few atoms thick. A fluorescent zinc-sulphide screen around the foil showed where the particles landed. Thomson's model predicted that all the particles would pass through with at most a tiny bend. What was actually seen is below.

Rutherford said that a very small, dense, positively charged nucleus at the centre holds almost all the mass, and the electrons revolve around it in circular paths, like planets round the Sun (the 'planetary model'). The nucleus is about 10⁻¹⁵ m across, against about 10⁻¹⁰ m for the whole atom. An atom is therefore mostly empty space. Rutherford won the Nobel Prize in Chemistry (1908) for his work on radioactivity; the gold-foil result came in 1911.

Why Rutherford's model failed. An electron moving in a circle is constantly accelerating, and by electromagnetic theory an accelerating charge must radiate energy. It would therefore lose energy, spiral inwards and crash into the nucleus within a tiny fraction of a second. The atom would not be stable, yet atoms are stable. The model also could not explain why hydrogen gives only certain line colours in its spectrum.

Bohr's model (1913). Niels Bohr kept the nucleus and added quantum ideas. (1) Electrons revolve only in certain fixed circular paths called orbits, shells or energy levels, and while in such an orbit they do not radiate energy. (2) Each orbit has a fixed energy; the orbits are numbered n = 1, 2, 3 … or named K, L, M, N, O … outward from the nucleus. (3) Only those orbits are allowed in which the angular momentum is a whole-number multiple of h/2π. (4) An electron jumps to a higher orbit by absorbing a fixed amount of energy and drops to a lower orbit by emitting it as light, with ΔE = hν. Bohr's model explained the line spectrum of hydrogen and was a landmark: he received the Nobel Prize in Physics in 1922.

After Bohr. Sommerfeld (1916) allowed elliptical orbits. Then de Broglie (1924) gave matter waves, Heisenberg (1927) the uncertainty principle (we cannot know the exact position and momentum of an electron together) and Schrödinger (1926) his wave equation. In the modern quantum-mechanical model, electrons do not have fixed paths; we speak instead of orbitals, regions where the electron is most likely to be found.

Two numbers fix the identity and the weight of every atom. The atomic number (Z) is the number of protons in the nucleus. It is the 'identity card' of an element: change the number of protons and you have a different element. In a neutral atom the number of electrons is also Z. The mass number (A) is the number of protons plus neutrons, that is, the number of nucleons. It is always a whole number. The number of neutrons is therefore A − Z. Henry Moseley (1913) showed through X-ray studies that atomic number, not atomic mass, is the fundamental property of an element, and this is why the modern periodic law is based on atomic number.

Worked example. Radhika is asked for the particles in sodium written as ²³₁₁Na (A = 23 at the top, Z = 11 at the bottom). Protons = Z = 11; electrons in the neutral atom = 11; neutrons = 23 − 11 = 12. For the ion Na⁺ the protons and neutrons stay 11 and 12, but the electrons fall to 10. Mass number and atomic mass are not the same: mass number is a whole number counting nucleons, while atomic mass (in u) is the average mass of the natural mixture of isotopes and is usually not a whole number.

Isotopes in detail. The word was coined by Frederick Soddy (1913), meaning 'same place' (in the periodic table). Isotopes of an element have the same number of electrons and therefore the same chemical properties, but different masses, so their physical properties (density, boiling point, rate of diffusion) differ slightly. F. W. Aston used the mass spectrograph to show that neon, for example, has isotopes of masses 20 and 22. Most elements occur as a mixture of isotopes, which is why atomic masses are not whole numbers. Chlorine occurs as ³⁵Cl and ³⁷Cl in the ratio about 3 : 1, so its average atomic mass is (35 × 3 + 37 × 1) ÷ 4 = 35.5 u. Hydrogen's three natural isotopes are protium, deuterium and tritium; heavier forms have been made only in laboratories and are extremely short-lived.

Separating isotopes. Because isotopes have the same chemistry, chemical reactions cannot separate them; we use their small difference in mass. In gaseous diffusion, uranium is first converted into the gas uranium hexafluoride (UF₆); by Graham's law the lighter gas molecules (with ²³⁵U) diffuse a little faster through porous barriers, and repeating this thousands of times enriches the mixture. Gas centrifuges and mass spectrometers also separate isotopes by mass. Natural uranium has less than 1 per cent ²³⁵U, so it must be enriched for many reactors and weapons. For the radioactive isotopes (radioisotopes) used in medicine and dating, see the chapter on Modern Physics.

The way electrons are arranged around the nucleus decides how an element behaves chemically. Bohr and Bury worked out a simple scheme for arranging electrons in shells (the Bohr-Bury scheme), and it works well for the first 20 elements. (1) A shell can hold at most 2n² electrons, where n is the shell number counted from the nucleus: K (n = 1) holds 2, L (n = 2) holds 8, M (n = 3) holds 18, N (n = 4) holds 32. (2) The outermost shell cannot hold more than 8 electrons (2 in the case of K), and the shell just inside it not more than 18. (3) Electrons fill the shells in order, starting from the one nearest the nucleus, and move to the next shell only when the inner one is full (strictly this holds up to calcium).

Valence electrons and valency. The electrons in the outermost shell are the valence electrons. Atoms are most stable when the outermost shell is full: 2 electrons (a duplet, as in helium) or 8 electrons (an octet, as in neon and argon). This is why the noble gases are unreactive, and why helium stays as single atoms. All other atoms react by losing, gaining or sharing electrons until they reach such a stable arrangement (the Kossel-Lewis idea, 1916). The valency of an element is the number of electrons its atom loses, gains or shares to complete the outer shell. If an atom has 1, 2 or 3 valence electrons (a metal), it usually loses them and valency = number of valence electrons (Na 1, Mg 2, Al 3). If it has 5, 6 or 7, it gains or shares and valency = 8 minus the number of valence electrons (N 3, O 2, Cl 1). Carbon, with 4, shares four electrons and has valency 4. Noble gases have valency zero.

Ions and isoelectronic species. When sodium (2, 8, 1) loses one electron it becomes Na⁺ (2, 8), which has the same arrangement as neon. Chlorine (2, 8, 7) gains one electron to become Cl⁻ (2, 8, 8), like argon. Particles with the same number of electrons are isoelectronic: N³⁻, O²⁻, F⁻, Ne, Na⁺, Mg²⁺ and Al³⁺ all have 10 electrons. The number of protons never changes in these processes. So Al³⁺ (Z = 13) has 13 protons and 13 − 3 = 10 electrons.

Quantum numbers (basics). In the modern model, each electron in an atom is described by four numbers, which together act like its address. The principal quantum number (n) = 1, 2, 3 … gives the shell, the size and the main energy (n = 1 is K, 2 is L, 3 is M). The azimuthal quantum number (l) takes values 0 to n − 1 and gives the sub-shell and its shape: l = 0 is s, 1 is p, 2 is d, 3 is f. The magnetic quantum number (m) takes values from −l to +l and gives the orientation of the orbital; a sub-shell therefore has 2l + 1 orbitals (s 1, p 3, d 5, f 7). The spin quantum number (s) is +½ or −½ and gives the direction in which the electron spins. An orbital can hold at most 2 electrons, so the sub-shells hold s 2, p 6, d 10 and f 14.