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A small dose of basic nuclear physics
It is well known that matter is made up of atoms. Atoms are built from three types of particle: protons (p), neutrons (n) and electrons (-e).
The mass of both neutrons and protons is ever so slightly higher than a unit mass (1 u = 1.66054 x 10-27 kg) on the atomic scale. Neutrons are electrically neutral, while protons each have a unit positive electrical charge and electrons a unit negative electrical charge. In a neutral atom, the positive charge from protons is balanced by an equal number of electrons, which are lighter, and have a mass of about 1/1836 of a proton.
The size of an atom is typically of the order of 10-10 m across. At the centre, there is a tiny nucleus (of about 10-15 m across) which is composed of neutrons and protons and contains all the positive charge of the atom. This charge is largely shielded by the surrounding electrons which orbit the nucleus and determine the chemical behaviour of an element. There is little influence exerted by one nucleus on the neighbouring nuclei. Radioactive decay is a spontaneous process. One nucleus cannot sense when another has decayed.
The nucleus contains closely packed neutrons and protons. The positively charged protons must exert a very strong repulsive force on each other according to Coulomb’s law, an inverse-square law. According to Newton’s law of gravitation, another inverse-square law, every particle that has mass attracts every other particle.
It turns out that although the gravitational force is more important on the astronomical scale, it is negligible on the nuclear scale and comes nowhere near to balancing the repulsive force which would blow the nucleus apart. Therefore there must be another attractive force, similar in magnitude to the electrostatic repulsive force, holding the nucleus together.
This attractive force between nucleons (neutrons and protons) is known as the strong interaction or strong force. The force has a number of very peculiar properties. It is exerted between immediate neighbouring nucleons in a nucleus, and does not extend beyond distances of a few femtometres (fm), where 1 fm = 10-15 m. For reference, neighbouring nuclei in a solid are 105 fm apart. Moreover, it does not depend on the charge of the nucleons. Importantly, this force is repulsive at very short range (less than 0.5 fm); otherwise the nucleons would be pulled together into a vanishingly small region of space which of course does not happen in practice.
Since nucleons remain bound in a stable nucleus, they must be in a low energy state. Inside the nucleus, they experience attractive forces on all sides from other nucleons, trapping them in a ‘potential energy well’. For protons, we must take account of the Coulomb repulsion. The superposition of this on the former modifies the potential well somewhat and effectively puts shoulders on the potential energy well.
Let us take some neutrons and some protons that are far apart from each other. We now allow them to come together to form a nucleus under the attractive influence of the strong nuclear force. When they have formed the nucleus, they are in lower energy state, having released energy – e.g. in the form of electromagnetic radiation. In order to pull the nucleons apart, one must supply energy, which is known as the binding energy. The binding energy of the nucleons is equal to the energy that was released in forming the nucleus. The higher the binding energy per nucleon in a nucleus, the more energy will be released during its formation. This manifests itself in the form of a difference of mass (or mass defect) which is related to energy by Einstein’s famous equation E = mc2, where E is the energy in joules, m is the mass in kg and c is the velocity of light in m/s. The total mass of the same number of nucleons is higher when they are separated as compared to that when they are tightly bound forming a nucleus.
The binding energy of nuclei increases roughly with their atomic mass. By studying binding energy per nucleons as a function of the number of nucleons or atomic mass (A), it is found that for most nuclides, this quantity is between 7 and 9 MeV per nucleon (see Figure 1). It has a peak for nuclides with an atomic mass of 60.
Fig. 1. Binding energy per nucleon
Near the peak of binding energy (for A = 60), the nuclei are most tightly bound. Remembering that the binding energy is energy that has been released in forming the nucleus, we can gain or release energy by transforming nuclei such that we ‘climb the curve of binding energy’ (see Figure 1). This can be done in two ways:
The first method is known as nuclear fusion link 1, where, for example, isotopes of hydrogen (deuterium and tritium) are fused, creating heavier elements like helium and producing energy in the process. The second method is known as nuclear fission, where heavy nuclei such as uranium-235 or plutonium-239 are broken down into lighter elements such as Kr-92 (krypton) and Ba-141 (barium), releasing energy in the process. The numbers refer to atomic masses of the respective isotopes. The mass balance equation in such nuclide transformations shows that the energy released is equal to the mass defect (loss of mass) as explained by Einstein’s equation.
Stable nuclei generally have the same number of protons and neutrons (or Z = N, where Z is the number of protons and N is the number of neutrons in the nucleus). This is more strictly observed for light nuclei with fewer than 20 protons (Z < 20) (see Figure 2). For heavier nuclei with more than 20 protons (Z > 20), with increasing number of protons, the rapid increase of coulomb repulsion force requires additional neutrons (to compensate the repulsion via the strong attractive force) for nuclear stability to be maintained. The most common combination of neutrons and protons for stable isotopes is ‘even-even’ (i.e. the nucleus contains an even number of protons and an even number of neutrons). There are only four stable nuclides that are ‘odd-odd’. In a chart of neutrons (N) versus protons (Z) for stable isotopes, a region of stability (shown by circles) can be drawn (see Figure 2).
Fig. 2 Regions showing the areas of stable and unstable isotopes
Why does the radioactive decay of nuclei take place?
Nuclear decay can occur if energy is released in the process, unless some external source of energy is made available. Each particle emitted in the decay process is released with some kinetic energy. The daughter nucleus has also recoil energy.In the plot of N versus Z for stable nuclei (Figure 2), the nuclides which lie above the region of stability are described as neutron-rich and they decay by β- emission which refers to negatively charged electrons. Nuclides which lie below the line of stability are described as proton-rich and they decay by β+ or α emission. The β+ particle is a positively charged electron and is known as positron or anti-electron. The α particle consists of two protons and two neutrons. During its emission both the number of protons and the number of neutrons of the resulting nucleus decrease by two. α and β decay are often accompanied by the emission of a γ electromagnetic photon. As this has no charge or mass it does not affect the number of protons and neutrons of the resulting nucleus.