Final answer:
A 100g sample of As-81 with a half-life of 33 seconds will decay to 6.25g in 132 seconds.
Step-by-step explanation:
The decay of a radioactive substance can be described by its half-life, which is the time it takes for half of the original sample to decay. In this case, the half-life of As-81 is given as 33 seconds. To find the time it takes for a 100g sample to decay to 6.25g, we can use the formula:
N = N0 * (1/2)^(t / T)
Where N is the final amount, N0 is the initial amount, t is the time passed, and T is the half-life. Rearranging the formula to solve for t:
t = T * log2(N / N0)
Substituting the values:
t = 33 seconds * log2(6.25g / 100g) = 33 seconds * log2(0.0625) = 33 seconds * (-4) = -132 seconds
Therefore, it would take 132 seconds for a 100g sample of As-81 to decay to 6.25g.