We are now in a position to be a little more quantitative about radioactive decay of nuclei and see what decay processes are allowed. All of the action in radioactive decay is in the nucleus, not in the electrons circulating the nucleus. The nucleus consists of equal numbers of protons and neutrons for the elements from helium to oxygen, except for beryllium, which has an extra neutron. In order to talk about radioactive nuclei a bit more simply, some terminology is in order. Physicists talk about the atomic number of an element, which is the number of protons (and also the number of electrons) in the atom and defines the element. It is given the sym­bol Z, which is used by physicists to indicate charge. Every element has a unique Z value that completely defines the chemical properties of the element because it defines the number of electrons, and electrons determine chemistry. The other important number to define a nucleus is the atomic mass, given by the symbol A. The atomic mass is just the number of protons and neutrons, so the number of neutrons is the atomic mass minus the atomic number or n = (A — Z).

For low Z elements, those with atomic number below about 15, the atomic mass is generally twice the atomic number, meaning that there are equal numbers of neutrons and protons. But as the atomic number gets larger, the number of neutrons increases rapidly. This is necessary because the repulsive force from the positive charge of the protons becomes too large as the nucleus gets bigger and the strong force that holds them together only operates over a very short distance, just on its immediate neighbors.4 By adding additional neutrons, the strong force is increased to hold the nucleus together.

A given element may exist in several versions, known as isotopes, with differ­ent numbers of neutrons but the same number of protons. Chemically the iso­topes are identical to each other so they cannot be separated by chemical means. Generally there are only one or a few isotopes of an element that are stable, and the other isotopes are unstable, or radioactive. Unstable isotopes undergo radio­active decay by emitting a, p, or у radiation, and they are often called radionuclides or radioisotopes.

Physicists have developed a shorthand notation to illustrate the isotopes and their radiation. The element is indicated by X, the atomic number (number of protons) is Z and the atomic mass (number of neutrons and protons) is A. The number of neutrons is just A — Z. A generic element and some examples of spe­cific elements and isotopes are:

AX 2He 126c 292U 2f2u 294Pu

Helium (He, also an a particle) and carbon (C) have equal numbers of protons and neutrons (2 each for He and 6 each for C), while the two uranium isotopes have a much larger number of neutrons than protons. Since the atomic number and the element name are redundant, it is convenient to shorten the notation in writing to just the element symbol and the atomic mass A, for example 238U, and it can also be written U-238. Uranium always has an atomic number of 92, so it does not have to be specified. Plutonium has an atomic number of 94, and the most common isotope has an atomic mass of 239.

As the Curies, Rutherford, and others learned, new elements are created when different isotopes undergo radioactive decay and emit a or p particles. There are some rules that govern these decay processes, which are conservation laws. In any radioactive decay, the charge Z is conserved, the total number of nucleons (pro­tons plus neutrons or A) is conserved, and energy is conserved. We have to take into account Einstein’s famous law (E = mc2) that energy and mass are equivalent and mass can be converted into energy, so it is really mass-energy that is con­served. In fact, mass is converted into pure energy, which is what gives radiation its energy.

The process of radioactive decay is a random, statistical process. It is impossible to say when a specific nucleus will undergo radioactive decay, but it is possible to measure how long it takes for half of the radioactive nuclei in a sample to decay. This is called the half-life, and it is characteristic of a particular radionuclide. Half-lives can vary from seconds to billions of years.

Let’s look at some examples of radioactive decay.5 Radium, the radionuclide isolated by Marie and Pierre Curie, has 88 protons and 138 neutrons for an atomic mass of 226, and it emits an a particle. Since an a particle is a helium nucleus, it has 2 protons and 2 neutrons. The total charge has to be conserved, so the decay product has to have 2 fewer protons than radium and an atomic mass that is 4 less than radium. Its decay scheme is:

288Ra -> 286Rn + 2a + energy

so radium decays into radon and emits an a particle, with a lot of energy given off in the process. The energy comes from the fact that the mass of the radium nucleus is greater than the sum of the masses of the radon and the a particle. It is generally the very heavy atoms that undergo a decay, such as radium, polonium, uranium, and plutonium. The total atomic mass and atomic number are equal on both sides of the arrow, so the conservation laws are upheld. In any a decay, the atomic number Z of the resulting nucleus is smaller by 2 and the atomic mass A is smaller by 4.

Now let’s consider a radionuclide that undergoes p decay. Recall that a p particle is equivalent to an electron, which has such a small mass in comparison to the nucleons that it is not considered in the decay equation. Becquerel first discov­ered radioactivity in his fortuitous experiment with a uranium salt, and it turns out that he was actually measuring p decay, though he didn’t know it at the time. Uranium consists primarily of the isotope 5’92U, which a-decays into 5^0Th (tho­rium). But thorium-234 itself is radioactive and it undergoes p decay, giving off an electron called a p particle. A problem immediately comes to mind. The electron has a negative charge but according to the conservation of charge rule, net charge cannot be created. What happens is that a neutron turns into a proton and an electron, thus conserving charge, and the electron comes flying out of the nucleus as a p particle.

It turns out not to be so simple, if that is indeed simple! Enrico Fermi, a bril­liant experimental and theoretical physicist from Italy, realized that the p particles had a broad distribution of energy, whereas the a particles emitted by a nucleus had a precise energy. Why does it matter? The energy of the particles coming out of radioactive decay depends on the change in mass of the nuclei and particles involved, according to E = mc2. The principle of conservation of energy seemed to be violated in the case of p decay since the ps did not have a specific energy but rather a range of energies. So Fermi postulated that another unknown particle, which he named a neutrino (“little neutral one” in Italian), must also be emitted with the remaining energy. Together the p and the neutrino had the exact energy needed. Neutrinos hardly interact with anything and they have an extremely small mass, so their existence was purely theoretical for a long time. The p decay of thorium is complex, so let’s look at a simple example of p decay, that of a natu­ral but fairly rare form of potassium, potassium-40 (or K-40; K is the symbol for potassium, from the neo-Latin word kalium). This reaction, by the way, is one of the natural ways in which you get exposed to radiation by eating foods rich in potassium, such as bananas (see Chapter 8).

19K -> 2°Ca + IP + v (antineutrino)

The charge on both sides of the equation add up properly (19 = 20 -1), the atomic mass is conserved because the p particle is not a nucleon and has very little mass, and energy is conserved because of the antineutrino. Fermi originally called it a neutrino, but when a proper theory was developed, it turned out to be an antineutrino, indicated by the bar above the symbol. The generic equation for P decay is:

n -> p+ + p- + v

Things get even weirder than this. In 1928 Paul Dirac had predicted that an electron should have an antiparticle called an antielectron, which is identical to an ordinary electron except it has a positive charge. It was later shown that all ele­mentary particles should have antiparticles with opposite properties. Any particle meeting its antiparticle ends up annihilating both particles and releasing pure energy (13). There is another type of p decay known as p+ decay that involves not an electron but an antielectron that has a positive charge and is called a positron, proving Dirac’s prediction. In this case, a proton turns into a neutron, a positron (P+) and a neutrino:

p+ ->n + p+ + v (neutrino)

A specific example of p+ decay is an isotope of oxygen that turns into nitrogen:

18O ■» + +1P + v

Things seem to be getting very strange here. We have positive and negative elec­trons, odd new particles called neutrinos and antineutrinos that are nearly impos­sible to observe, neutrons and protons that turn into each other, and quarks with partial charges that make up neutrons and protons! Can we make any sense out of this? Perhaps we cannot, but the theories are quite well developed to explain these odd events. Fermi explained p decay by postulating a new force called the weak force that acts over extremely small distances in the nucleus. It is weak in comparison to the strong force that holds neutrons and protons together. Fermi’s theory predicted the creation of neutrinos and antineutrinos and showed that neutrons and protons could decay according to the equations given above by creating electrons and neu­trinos or their antiparticles. But it was not a complete theory. It was a theory sort of like Bohr’s theory of the atom before quantum mechanics was developed. In 1958, Richard Feynman and Murray Gell-Mann revised Fermi’s theory substantially and predicted the occurrence of new particles called W bosons that were produced in the process of neutron or proton decay and which then decay into electrons and neutrinos. These particles were later discovered in high-energy accelerators. In 1967, Steven Weinberg and Abdus Salam independently proposed a complete theory that united the electromagnetic force that explains charged-particle interactions and the weak force that explains p decay. This theory is known as the electroweak theory and, as you might guess, it predicted other particles that have subsequently been found (9).

Now you know where a and p radiation come from and how they are produced in radioactive decay processes. But where does у radiation come from? One way to think about the nucleus is that it also can have quantized energy levels like those of the electrons in the Bohr atom. A nucleus is normally in its lowest energy level, or ground state. When it undergoes radioactive decay by emitting an a or P particle, the nucleus is often left in an excited state at a higher energy level. The nucleus will then adjust to its ground level state by emitting a у ray that takes off the energy, just like the photon that is given off when an electron jumps from one energy level to a lower one. Many, but not all, radioactive nuclei emit not only an a or p particle but also a у ray when they decay. A у ray is also a photon, but by definition it comes only from the nucleus. X-rays come from electrons jump­ing between energy levels in an atom or from electrons moving at high speed and then abruptly being deflected or stopping when they hit atoms. That is how Rontgen produced X-rays in his evacuated tubes. There is no fundamental differ­ence between у rays and X-rays, only the way in which they are produced.