Nuclear stability is determined by the competition between two fundamental interactions. Atomic nuclei consist of protons and neutrons, which attract each other through the nuclear force, while protons repel each other via electromagnetic force due to their positive charge. These two forces compete, leading to various stability of nuclei. There are only certain combinations of neutrons and protons which form stable nuclei. Neutrons stabilize the nucleus because they attract each other and protons, which helps offset the electrical repulsion between protons. As a result, as the number of protons increases, an increasing ratio of neutrons to protons is needed to form a stable nucleus. Suppose there are too many (neutrons also obey the Pauli exclusion principle) or too few neutrons for a given number of protons. In that case, the resulting nucleus is not stable, and it undergoes radioactive decay. Unstable isotopes decay through various radioactive decay pathways, most commonly alpha decay, beta decay, or electron capture. Many other rare types of decay, such as spontaneous fission or neutron emission, are known.
The Pauli exclusion principle also influences the critical energy of fissile and fissionable nuclei. For example, actinides with odd neutron numbers are usually fissile (fissionable with slow neutrons), while actinides with even neutron numbers are not fissile (but fissionable with fast neutrons). Due to the Pauli exclusion principle, heavy nuclei with an even number of protons and an even number of neutrons are very stable thanks to the occurrence of ‘paired spin.’ On the other hand, nuclei with an odd number of protons and neutrons are mostly unstable.
Magic Numbers of Protons and Neutrons
A magic number is many nucleons in a nucleus, corresponding to complete shells within the atomic nucleus. Atomic nuclei consisting of such a magic number of nucleons have a higher average binding energy per nucleon than one would expect based upon predictions such as the mass formula of von Weizsaecker (also called the semi-empirical mass formula – SEMF) and are hence more stable against nuclear decay. Magic numbers are predicted by the nuclear shell model. They are proved by observations showing that there are sudden discontinuities in the proton and neutron separation energies at specific values of Z and N. These correspond to the closing of shells (or sub-shells). Nuclei with closed shells are more tightly bound than the next higher number. The closing of shells occurs at Z or N = 2, 8, 20, 28, (40), 50, 82, 126. It is found that nuclei with even numbers of protons and neutrons are more stable than those with odd numbers. Nuclei that have both neutron numbers and proton numbers equal to one of the magic numbers can be called “doubly magic” and are found to be particularly stable.There are further special properties of nuclei, which have a magic number of nucleons:
- Higher abundance in nature. For example, helium-4 is among the most abundant (and stable) nuclei in the universe.
- The stable elements at the end of the decay series all have a “magic number” of neutrons or protons. The nuclei He-4, O-16, and Pb-208 (82 protons and 126 neutrons) that contain magic numbers of both neutrons and protons are particularly stable. The relative stability of these nuclei is reminiscent of that of inert gas atoms (closed electron shells).
- Nuclei with N = magic number have lower neutron absorption cross-sections than surrounding isotopes.
- These nuclei appear perfectly spherical in shape; they have zero quadrupole electric moments.
- Magic number nuclei have higher first excitation energy.
Unstable Nuclei-Decay Modes
Nuclear decay (Radioactive decay) occurs when an unstable atom loses energy by emitting ionizing radiation. Radioactive decay is a random process at the level of single atoms, in that, according to quantum theory, it is impossible to predict when a particular atom will decay. During radioactive decay, an unstable nucleus spontaneously and randomly decomposes to form a different nucleus (or a different energy state – gamma decay), giving off radiation in the form of atomic particles or high-energy rays. This decay occurs at a constant, predictable rate that is referred to as half-life. A stable nucleus will not undergo this kind of decay and is thus non-radioactive. There are many modes of radioactive decay:
- Alpha radioactivity. Alpha decay is the emission of alpha particles (helium nuclei). Alpha particles consist of two protons and two neutrons bound together into a particle identical to a helium nucleus. Because of its very large mass (more than 7000 times the mass of the beta particle) and its charge, it heavy ionizes material and has a very short range.
- Beta radioactivity. Beta-decay is the emission of beta particles. Beta particles are high-energy, high-speed electrons or positrons emitted by certain types of radioactive nuclei such as potassium-40. The beta particles have a greater range of penetration than alpha particles but still much less than gamma rays. The beta particles emitted are a form of ionizing radiation, also known as beta rays. The production of beta particles is termed beta decay.
- Gamma radioactivity. Gamma radioactivity consists of gamma rays. Gamma rays are electromagnetic radiation (high energy photons) of a very high frequency and high energy. They are produced by the decay of nuclei as they transition from a high-energy state to a lower state known as gamma decay. Gamma emissions accompany most nuclear reactions.
- Neutron emission. Neutron emission is a type of radioactive decay of nuclei containing excess neutrons (especially fission products), in which a neutron is ejected from the nucleus. This type of radiation plays a key role in nuclear reactor control because these neutrons are delayed neutrons.
The rate of nuclear decay is also measured in terms of half-lives. The half-life is the amount of time it takes for a given isotope to lose half of its radioactivity. Half-lives range from millionths of a second for highly radioactive fission products to billions of years for long-lived materials (such as naturally occurring uranium). Notice that short half-lives go with large decay constants. Radioactive material with a short half-life is much more radioactive (at the time of production) but will lose its radioactivity rapidly. No matter how long or short the half-life is after seven half-lives have passed, less than 1 percent of the initial activity remains.