The beta decay of cesium-137 has a half-life of 30.0 years.How many years must pass to reduce a 30 mg sample of cesium 137 to 5.2 mg?

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Quizplus · Accepted Answer

To find the number of years it takes for a 30 mg sample of cesium-137 to decay to 5.2 mg, we use the half-life formula. The half-life of cesium-137 is 30 years, meaning every 30 years, the amount of cesium-137 halves. To find the number of half-lives (n) that have passed, we use the formula: $ \text{final amount} = \text{initial amount} \times \left(\frac{1}{2}\right)^n $. Rearranging for n gives us $ n = \log_{\frac{1}{2}} \left(\frac{\text{final amount}}{\text{initial amount}}\right) $. Plugging in the given values, $ n = \log_{\frac{1}{2}} \left(\frac{5.2}{30}\right) $. This gives approximately 2.53 half-lives. Multiplying this by the half-life duration (30 years) gives us approximately 76 years.

The Beta Decay of Cesium-137 Has a Half-Life of 30