- 1). Key .5 into your calculator and press the "ln" key to take the natural logarithm of .5.
- 2). Divide by the half-life of the element and press the equals key. The result is the element's decay constant. For example, the half-life of cesium-137 is 30 years. Taking the natural log of .5 and dividing by 30 gives --0.023.
- 3). Multiply the decay constant by a time interval. Using the cesium-137 example and 10 years, 10 times --0.023 equals --0.23.
- 4). Press the "e^x" key on the calculator to take the natural antilog of the result. From the example, e^(-0.23) = .79. This is the fraction of radioactive cesium-137 that remains after 10 years. Multiplying by 100 gives 79 percent.
- 5). Enter a fraction for which you wish to find the number of years. Press the "ln" key to take the natural log of this number. Divide by the decay constant of the substance. For example, find the amount of time it takes for cesium-137 to decay to 10 percent of its original amount. Ln(.1) divided by --0.023 years = 100 years.
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