The half-life of a substance that undergoes decay is the time it takes for a substance to shrink by half. It was initially used to describe the decay process of radioactive elements, such as uranium or plutonium. However, it can be used for any substance that undergoes a decay, according to a certain index, or exponential. This article explains how to calculate the half-life of any substance by knowing its decay rate, in other words the initial amount of the substance and the amount left after a certain time interval.
Steps
Method 1 of 1: Calculating the half-life
Calculate Half Life Step 1
Step 1. Divide the amount of substance at a given point by the amount left over after a specific time interval
For example, if you have 1500 grams at the beginning, and 1000 grams at the end, the starting amount divided by the final amount is 1.5
Calculate Half Life Step 2
Step 2. Calculate the decimal logarithm (log) of the result obtained using a scientific calculator
The logarithm of a number is the exponent to which the base must be raised (or the number of times the base must be multiplied by itself) to get the number itself. The base of the decimal logarithm is 10. The log button on a calculator is the decimal logarithm.
For example, the decimal logarithm of 1, 5 is 0, 176. This means that 10 raised to 0, 176 gives 1, 5.
Calculate Half Life Step 3
Step 3. Multiply the elapsed time by the decimal logarithm by 2, or 0, 30103
For example, if the elapsed time is 100 minutes, multiply 100 by 0, 30103. The result is 30, 103
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