﻿ Half-Lives and Radioactive Dating - Nuclear Chemistry - Chemistry Essentials for Dummies ﻿

## Chemistry Essentials for Dummies

Chapter 4. Nuclear Chemistry

If you could watch a single atom of a radioactive isotope, U-238, for example, you wouldn’t be able to predict when that particular atom might decay. It may take a millisecond, or it may take a century. There’s simply no way to tell.

But if you have a large enough sample — what mathematicians call a statistically significant sample size — a pattern begins to emerge. It takes a certain amount of time for half the atoms in a sample to decay. It then takes the same amount of time for half the remaining radioactive atoms to decay, and the same amount of time for half of those remaining radioactive atoms to decay, and so on. The amount of time it takes for one-half of a sample to decay is called the half-life of the isotope, and it’s given the symbol t1/2. Table 4-1 shows this process.

Table 4-1. Half-Life Decay of a Radioactive Isotope

 Number of Half-Lives Percent of the Radioactive Isotope Remaining 0 100.00 1 50.00 2 25.00 3 12.50 4 6.25 5 3.13 6 1.56 7 0.78 8 0.39 9 0.20 10 0.10

WARNING! The half-life decay of radioactive isotopes is not linear. For example, you can’t find the remaining amount of an isotope at 7.5 half-lives by finding the midpoint between 7 and 8 half-lives.

If you want to find times or amounts that are not associated with a simple multiple of a half-life, you can use this equation:

In the equation, ln stands for the natural logarithm (the base e log, not the base 10 log; it’s that In button on your calculator, not the log button). No is the amount of radioactive isotope that you start with (in grams, as a percentage, in the number of atoms, and so on), N is the amount of radioisotope left at some time (t), and t1/2 is the half-life of the radioisotope. If you know the half-life and the amount of the radioactive isotope that you start with, you can use this equation to calculate the amount remaining radioactive at any time.