Radon is a radioactivegas that can be trapped in the basement of homes, and its
ID: 1728121 • Letter: R
Question
Radon is a radioactivegas that can be trapped in the basement of homes, and its presencein high concentration is a known heath hazard. Radon has ahalf-life of 3.83 days. A gas sample contains 4.00 X108 radon atomsinitially. How many atoms will remain after 14.0 days have passedif no more radon leaks in? How long before 99% of the samplehas decayed? Please work the problem out all the way so I can fullyunderstand it :) Thank You!! Radon is a radioactivegas that can be trapped in the basement of homes, and its presencein high concentration is a known heath hazard. Radon has ahalf-life of 3.83 days. A gas sample contains 4.00 X108 radon atomsinitially. How many atoms will remain after 14.0 days have passedif no more radon leaks in? How long before 99% of the samplehas decayed? Please work the problem out all the way so I can fullyunderstand it :) Thank You!!Explanation / Answer
Half-life is the the time it takes for one-half of a sample todecay. Each half-life after that, half of what remainsdecays, and so on. The formula for the fraction remaining forhalf-life k is: A = 2-t/k Solve for A after 14 days: A = 2-(14d/3.83d) = 2-3.655 = 0.079 With 4.00*108 radon atoms initially, then we have (0.079)*(4.00*108) = 3.16*107 radon atomsafter 14 days. To compute the time needed for 99% of the sample to decay, we haveto solve the original formula for t: A = 2-t/k ln(A) = (-t/k)*ln(2) t = (-k)*ln(A)/ln(2) Plug in our values: t = (-3.83d)*ln(1 - 0.99)/ln(2) t = (-3.83d)*ln(0.01)/0.6931 t = (-3.83d)*(-4.605)/0.6931 = 25.45 days
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