We come now to a most important question, one that will lead us to the idea of radioactivity: What is it that determines which isotopes a given element will have? For example, uranium has isotopes weighing 235 and 238. Small amounts of U²³⁴ and U²³⁶ are also found in nature. Why do we not find U²³², U²³³, U²³⁷ or U²³⁹? Evidently only certain numbers of neutrons will hang together with 92 protons.
Consider another example, this time of the lightest known element, hydrogen. We have already mentioned two isotopes of hydrogen: light hydrogen with weight 1 (symbolized H¹), having a nucleus consisting of a single proton and no neutrons, and heavy hydrogen (also called deuterium) of weight 2 (H²), having one proton and one neutron. The latter isotope occurs as only about one part in 5,000 of natural hydrogen. There is also a slight trace of tritium (H³), having one proton and two neutrons. But here the sequence stops. What has happened to H⁴, H⁵, H⁶, etc?
This question is related to the earlier one: why there are no atoms in nature of charge 43, 61, 85, and 87, and why there are none with charges greater than 92. To answer these questions requires a little knowledge about the laws which govern the motion of neutrons and protons within the nucleus, and the nature of the forces which are exerted by a neutron on a neutron, a neutron on a proton, and a proton on a proton.
The motion of neutrons and protons within the nucleus is governed by the same laws which govern the motion of electrons within the atom. For both the nucleus and the atom there is a ground state of motion which has more stability (less energy) than any other state. Of course the arrangement and motion of electrons in the atom depend not only on this general rule but also on the specifically electrical nature of the forces which act between the electrons and the nucleus. In the same way the arrangement and motion of the neutrons and protons within the nucleus depend upon the nature of the forces which act between neutrons and protons.
These forces are definitely not of gravitational origin. Gravitational attraction is extremely weak compared to the attraction between neutrons and protons, and is utterly negligible in the realm of nuclear phenomena. Neither can the nuclear forces be electrical in origin. The neutrons are electrically neutral; and the protons actually repel each other by virtue of their electrical charge. The nuclear forces are something entirely new. They are the strongest forces yet encountered, and they are without a counterpart in the macroscopic world.
Nuclear forces are not yet completely understood. But to understand nuclear stability we need to know only one peculiar fact governing the behavior of neutrons and protons (and incidentally also electrons): They want to be different. To each particle a state or pattern of motion can be assigned. When any two neutrons are compared, their pattern of motion must be essentially different. The same holds for any two protons. A neutron and a proton, however, may be found in similar patterns since they differ anyway in their charge.
Now among the possible patterns of motion some have lower and some have higher energies. Individual neutrons and protons will first occupy the lowest energy states, in accordance with the rule of least energy for maximum stability. Then the demand for a difference will force subsequent particles into patterns of higher and higher energies.
Since a neutron does not exclude a proton from being in the same pattern, the lowest energy state may be occupied simultaneously by one neutron and one proton.[4] If another neutron or proton is added, it must be put into the next state of higher energy. For this reason we would expect that nuclei are most stable when they contain an equal or nearly equal number of neutrons and protons. For nuclei which are not too heavy, this is indeed the case. For example, nitrogen, which has seven protons, has two stable isotopes, N¹⁴ and N¹⁵, with seven and eight neutrons respectively. For heavy nuclei, however, the situation is a little different.
The nuclear force between neutrons and protons acts only over a very short range—the particles must almost be in contact with each other in order to experience a sizeable attraction. Consequently a neutron or a proton interacts only with its immediate neighbors in the nucleus. The electrical repulsion between the protons, however, acts over a much longer range. A proton is repelled by all the other protons in the nucleus. For heavy nuclei this repulsion is sufficient to reduce the number of protons relative to the number of neutrons. Lead, for example, with 82 protons, has four stable isotopes, with 122, 124, 125, and 126 neutrons.
We have said that seven protons will combine stably with seven or eight neutrons. What happens if seven protons are combined with six or nine neutrons (to make N¹³ or N¹⁶)? Our rule does not prevent them from sticking together; it says only that these combinations would be more stable if a proton could be converted into a neutron (in the case of six) or a neutron into a proton (in the case of nine).