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