Sadije has taught high school physics and physical science. She has a bachelor’s in physics and a master’s in biomedical engineering.

In this lesson, you will learn about radioactive decay and related calculations. You will also learn to predict what type of radioactive decay a particular nucleus will undergo.

## Radioactive Decay of a Single Atom

What do a gumball machine and a radioactive material have in common? The answer is statistics. Although the mathematics dealing with these two processes may be different, the general idea is the same. Whether a gumball machine will dispense a specific gumball and whether a specific atom in a radioactive material will spontaneously undergo radioactive decay are both inquiries that are determined by probability.

When dealing with nuclear decay mathematically, we are most interested in looking at the number of atoms in a certain material that will decay over a particular period of time. These calculations will not reveal which specific atoms in a material will spontaneously decay, just how many will decay. Going back to the gumball machine analogy, this would be like calculating how many gumballs are left in a gumball machine after a certain amount of time, rather than paying attention to whether a particular gumball will be dispensed. The equations pictured below are utilized to gleam such information. A key thing to remember is that the unit for time and the unit for half-life must be the same (both is seconds, both in minutes, both in hours, etc).

It is possible to determine which type of decay a particular radioactive material will undergo by observing a few general trends. For beta (β) decay, this information is gleamed by looking at the ratio of neutrons (N) to protons (Z) in an isotope. For elements with an atomic number less than 20, an N/Z ratio of 1 indicates that an isotope is stable. Isotopes with an N/Z ratio that is larger than 1, which corresponds to an excess number of neutrons, will undergo beta decay. For elements with a larger atomic number, stable nuclei occur at N/Z ratios above 1 and up to 1.5. Alpha (α) decay is somewhat easier to predict. Heavy elements, which are elements with atomic numbers greater than 83, are all unstable and are most likely to undergo alpha decay. Gamma (γ) decay is a bit different, in that it does not cause an isotope to change its atomic number or its mass. Gamma decay is just a method of releasing excess energy. Gamma decay occurs when a nucleus is in an excited state (this correlates to the locations of protons and neutrons in the nucleus) and needs to release energy to become stable. It can occur in conjunction with another type of decay or as a stand alone process that occurs after another type of decay has occurred.

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