What percent of a given mass of a radioactive substance will be left and decade after four half lives?
Answers
The most likely amount is 1/16 or 6.25%, but there is also a probability curve as to other outcomes. By definition, a half life does not guarantee that exactly half of the radioactive atoms will always undergo decay in the time period. But when speaking about very large numbers of atoms, the amount of deviation becomes very small due to the law of large numbers. For example, if you have just four atoms, what are the various probabilities that 1, 2 or 3 will have undergone decay in one half life period? It is not 0%, 50% and 0%, but rather 25%, 37.5% and 25% (with zero or four each at 6.25%). But if we are talking about billions of atoms, the likelihood that the amount that have decayed in a half life will vary measurably from 50% is vanishingly small.