The alpha particle needs some extra energy to escape. According to the laws of older physics there is no possibility for it to obtain this extra energy and therefore escape is impossible. But the more newly discovered laws governing the motion of neutrons and protons (the laws of quantum mechanics) are not so stringent; they permit the alpha particle to use “borrowed” energy to overcome the energy barrier. Of course the alpha particle must always repay the loan—which it can easily do out of the large fund of electric energy that is released when it gets out of the repulsive range of the residual nucleus. There is no interest on the loan. Such energy loans are not automatically granted in nature. There are two factors which make the loan improbable: if the amount is big or if the term is long. These restrictions effectively limit the particles which may apply for an energy loan. Objects of great size and weight are unable to qualify, but the small particles of the atomic world often do. The more energy carried off by the alpha particle after the alpha decay, the less energy must be borrowed in order to overcome the barrier, and the more rapidly the decay may be expected to occur. So sensitive is the decay to the energy of the alpha particle, that an alpha particle carrying twice the energy is emitted a hundred trillion times fester. Half-lives for alpha decay vary from a fraction of a second to billions of years. But even the shortest half-life for alpha decay is remarkably long compared to the time required for the alpha particle to cross the nucleus. This means that the alpha particle makes a tremendous number of attempts to escape from the nucleus before it actually succeeds. According to the older classical theory the alpha process should never occur, and in fact it occurs with a very small probability. A single alpha decay is not usually a sufficient process to bring about stability of the daughter nucleus. A whole chain of radioactive decays is usually required before stability is achieved. Most nuclei which emit alpha particles belong to one of these radioactive decay chains. The heavy nuclei for which alpha decay occurs all contain a large excess of neutrons. Since the alpha particle carries off exactly two neutrons and two protons, the ratio of the number of neutrons to the number of protons is increased in the daughter nucleus. This has an unstabilizing influence. (Actually, in lighter nuclei stability requires that the ratio of neutrons to protons be closer to unity.) The daughter nucleus is thus apt to be beta-active, converting a neutron into a proton (plus an electron and a neutrino) in order to decrease its ratio of neutrons to protons. In this way a chain of radioactive decays may occur, more or less alternating between alpha and beta emissions, with gamma rays being occasionally emitted also.