Concepts: Nuclear size, composition and atomic masses

2.1 A small, heavy centre

The previous chapter showed that the positive charge and almost all the mass of an atom sit in a tiny central nucleus. Alpha-particle scattering put the nuclear radius smaller than the atomic radius by a factor of about ten thousand. Scale an atom up to a classroom and its nucleus shrinks to a pinhead. The volume of the nucleus is therefore only about 10 to the -12 of the atomic volume, so the atom is almost entirely empty. In spite of that, more than 99.9 per cent of the atomic mass is inside the nucleus.

2.2 What the nucleus contains

A nucleus is made of protons and neutrons, together called nucleons. The proton carries a positive charge equal in size to the electron's charge and has a mass of 1.67262 × 10 to the -27 kg, or 1.00727 u. The neutron carries no charge and weighs almost what a proton does. Z counts the protons; A counts protons plus neutrons; therefore N = A - Z counts the neutrons. A nuclear species is written as A above Z before the chemical symbol of the element.

Nuclear species fall into families. Isotopes have the same Z but different N; isobars have the same A but different Z; isotones have the same N but different Z. Most elements occur naturally as a mixture of isotopes.

2.3 The atomic mass unit

Atomic masses are far too small to be expressed comfortably in kilograms. A carbon-12 atom has a mass of 1.992647 × 10 to the -26 kg, so the kilogram is an awkward unit at this scale. The atomic mass unit is defined as one twelfth of the mass of a carbon-12 atom, which works out to 1.660539 × 10 to the -27 kg. On this scale the proton is 1.00727 u and the neutron 1.00866 u.

The usefulness of the unit shows up in how closely atomic masses follow whole numbers. The mass of a hydrogen atom is 1.00783 u, and many atomic masses are close to integral multiples of it. The exceptions are real. Chlorine, for example, has atomic mass 35.46 u because it is a mixture of two isotopes of masses 34.98 u and 36.98 u with relative abundances of 75.4 and 24.6 per cent; the weighted average is 35.47 u. Mass spectrometers measure these masses precisely and reveal the isotope mixture. Hydrogen itself has three isotopes: the lightest, with abundance 99.985 per cent, is the proton; the other two are deuterium and tritium.

2.4 Nuclear radius and density

Electron scattering and other experiments show that the radii of nuclei fit

R = R0 A to the power one-third, with R0 about 1.2 fm.

Because the volume of a sphere goes as the cube of the radius, the volume grows in proportion to A. The mass also grows in proportion to A, so the ratio of mass to volume, the nuclear density, stays nearly the same for all nuclei, of the order of 10 to the 17 kg per cubic metre. This is why the chapter can speak of nuclear matter density as a material property rather than a per-nucleus number. It also explains why the nuclear radius does not grow linearly with the number of nucleons: adding eight nucleons to a light nucleus changes the radius much more than adding eight to a heavy one.

2.5 Reading the mass spectrometer data

The isotope picture explains why atomic masses are not integers even though nuclear masses are close to them. A mass spectrometer separates atoms by mass and records the abundance of each mass value, so a single element shows up as a set of peaks. The average mass is then the abundance-weighted mean, which is the number printed in the periodic table. In problems, the average mass is used when the element is treated as a mixture, while a single isotope's mass is used when the problem names that isotope explicitly.

2.6 Charge, mass and the size of the nucleus

The nucleus holds a charge of +Z e in a volume that grows only as A, so the charge density is nearly uniform too. For light nuclei the number of neutrons is close to the number of protons, and the neutron excess grows with A because it takes more neutral particles to soften the Coulomb repulsion among many protons. This is why heavy stable nuclei have neutron-to-proton ratios near three to two.