## The Random Nature of Radioactive Decay

We cannot tell electrons apart. All electrons have the same mass, the same charge. All electrons in the ground state in the atom of which they are a part all have the same energy, if the atom is the same element. In the same sense, we cannot tell atoms apart. If two atoms are the same element, with the same number of neutrons, both in the ground state, we cannot say which is which.

If an element is radioactive, made up of atoms, all in the same state, then we cannot say at any point which atom will decay in the next time period. All atoms will decay with equal probability. Radioactive decay is a truly random process, not affected by any external conditions – pressure, temperature etc. Although the process of decay is a random process, we can make useful predictions. If we start with a large number of atomswe can expect a certain number to decay in the next time period. Ifwere larger we would expect more decays. On average the rate of decay is proportional to the number of atoms in the sample. We can write

whereis a constant, called the decay constant. The – sign indicates thatis decreasing.

By writingwe can see can see that in a time(whereis infinitesimally small) a fractionof theatoms present will decay on average. This is a prediction. If we have lots of samples, all withatoms initially, sometimes slightly more atoms will decays, sometimes slightly less.