The radioactive isotope of lead, pb-209, decays at a rate proportional to the amount present at time t and has a half life of 3.3 hours. if 1 gram of this isotope is present initially, how long will it take for 90% to decay?

We can calculate how long will it take 90% to decay by using the half-life equation. It is expressed as:

A = Ao e^-kt

where A is the amount left at t years, Ao is the initial concentration, and k is a constant.

From the half-life data, we can calculate for k.

1/2(Ao) = Ao e^-k(3.3)
k = 0.21

.10Ao = Ao e^- 0.21(t)
t = 10.96 hrs

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