Why Does Radioactive Decay Occur?

Radioactive decay a the spontaneous process through which an unstable atomic nucleus breaks into smaller, more stable fragments. Have you ever wondered why some nuclei decay while others don't?

It's basically a matter of thermodynamics. Every atom seeks to be as stable as possible. In the case of radioactive decay, instability occurs when there is an imbalance in the number of protons and neutrons in the atomic nucleus. Basically, there is too much energy inside the nucleus to hold all the nucleons together. The status of the electrons of an atom doesn't matter for decay, although they, too, have their own way of finding stability. If the nucleus of an atom is unstable, eventually it will break apart to lose at least some of the particles that make it unstable. The original nucleus is called the parent, while the resulting nucleus or nuclei are called the daughter or daughters. The daughters might still be radioactive, eventually breaking into more parts, or they might be stable.

Three Types of Radioactive Decay

There are three forms of radioactive decay: which of these an atomic nucleus undergoes depends on the nature of the internal instability. Some isotopes can decay via more than one pathway.

Alpha Decay

In alpha decay, the nucleus ejects an alpha particle, which is essentially a helium nucleus (two protons and two neutrons), decreasing the atomic number of the parent by two and the mass number by four.

Beta Decay

In beta decay, a stream of electrons, called beta particles, are ejected from the parent, and a neutron in the nucleus is converted into a proton. The mass number of the new nucleus is the same, but the atomic number increases by one.

Gamma Decay

In gamma decay, the atomic nucleus releases excess energy in the form of high-energy photons (electromagnetic radiation). The atomic number and mass number remain the same, but the resulting nucleus assumes a more stable energy state.

Radioactive vs. Stable

A radioactive isotope is one that undergoes radioactive decay. The term "stable" is more ambiguous, as it applies to elements that don't break apart, for practical purposes, over a long span of time. This means stable isotopes include those that never break, like protium (consists of one proton, so there's nothing left to lose), and radioactive isotopes, like tellurium -128, which has a half-life of 7.7 x 10²⁴ years. Radioisotopes with a short half-life are called unstable radioisotopes.

Some Stable Isotopes Have More Neutrons Than Protons

You might assume that a nucleus in stable configuration would have the same number of protons as neutrons. For many lighter elements, this is true. For example, carbon is commonly found with three configurations of protons and neutrons, called isotopes. The number of protons does not change, as this determines the element, but the number of neutrons does: Carbon-12 has six protons and six neutrons and is stable; carbon-13 also has six protons, but it has seven neutrons; carbon-13 is also stable. However, carbon-14, with six protons and eight neutrons, is unstable or radioactive. The number of neutrons for a carbon-14 nucleus is too high for the strong attractive force to hold it together indefinitely.

But, as you move to atoms that contain more protons, isotopes are increasingly stable with an excess of neutrons. This is because the nucleons (protons and neutrons) aren't fixed in place in the nucleus, but move around, and the protons repel each other because they all carry a positive electrical charge. The neutrons of this larger nucleus act to insulate the protons from the effects of each other.

The N:Z Ratio and Magic Numbers

The ratio of neutrons to protons, or N:Z ratio, is the primary factor that determines whether or not an atomic nucleus is stable. Lighter elements (Z < 20) prefer to have the same number of protons and neutrons or N:Z = 1. Heavier elements (Z = 20 to 83) prefer an N:Z ratio of 1.5 because more neutrons are needed to insulate against the repulsive force between the protons.

There are also what are called magic numbers, which are numbers of nucleons (either protons or neutrons) that are especially stable. If both the number of protons and neutrons have these values, the situation is termed double magic numbers. You can think of this as being the nucleus equivalent to the octet rule governing electron shell stability. The magic numbers are slightly different for protons and neutrons:

• Protons: 2, 8, 20, 28, 50, 82, 114
• Neutrons: 2, 8, 20, 28, 50, 82, 126, 184

To further complicate stability, there are more stable isotopes with even-to-even Z:N (162 isotopes) than even-to-odd (53 isotopes), than odd-to-even (50) than odd-to-odd values (4).

Randomness and Radioactive Decay

One final note: Whether any one nucleus undergoes decay or not is a completely random event. The half-life of an isotope is the best prediction for a sufficiently large sample of the elements. It can't be used to make any sort of prediction on the behavior of one nucleus or a few nuclei.

Can you pass a quiz about radioactivity?