How to Calculate the Half-Life of an Isotope

Find the half-life of an isotope by using the rate of decay.

A half-life is the amount of time it takes for half of a chemical sample to decay. Half-lives are used to find the age of samples and the amount of a sample remaining. Finding the half-life of an isotope is similar to finding the half-life of other elements. Isotopes are elements on the periodic table that have the same number of electrons and protons, however, they have different amounts of neutrons. Therefore, they have different rates of decay.

Things You'll Need

• Calculator

Instructions

1. Solve for the natural logarithm, or the "LN," of 1/2. This expresses that 50 percent of the original amount of the isotope has decayed.

2. Find the rate of decay for the isotope. The rate of decay is equal to the isotope's negative rate constant.

3. Divide the value found in Step 1 by the isotope's rate of decay found in Step 2. This value is the half-life of the isotope.

References

• Purdue: Determination and Use of the Half-Life
• UCSD: Exponential Growth and Decay
• Math Central; Exponential Decay; Natasha Glydon