The amount of 228Ac in a sample decreases to one eighth (18) of its original value in about 18 hours due to β-decay. Estimate the half-life of 228Ac.[1]b
Question
The amount of 228Ac in a sample decreases to one eighth (18) of its original value in about 18 hours due to β-decay. Estimate the half-life of 228Ac.[1]b
Solution
The half-life of a radioactive substance is the time it takes for half of the substance to decay. In this case, the substance is 228Ac and it decays to one eighth of its original value in 18 hours.
Step 1: Determine the number of half-lives in 18 hours Since one eighth is 2^-3, this means that three half-lives have occurred in 18 hours.
Step 2: Calculate the half-life To find the half-life, divide the total time by the number of half-lives. So, 18 hours divided by 3 gives a half-life of 6 hours for 228Ac.
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