How long will it take for 99.9% of a 0.00570 mg sample of radioactive phosphorus-32 to decay?

Question

How long will it take for 99.9% of a 0.00570 mg sample of radioactive phosphorus-32 to decay? The half-life of phosphorus-32 is 14.30 days, so give your answer in days.

Thanks so much!!!

Answer 1

The half life is the time it takes 50% of the sample to decay.

So every 14.3 days 50% of what remains will decay.

Therefore, the problem you need to solve is the following:

(.5)^X = (1-.999) solve for X where

X is the number of half lives it will take for 99.9% of the sample to decay. The final answer in days = X half lives*14.3 days/half life

X = ln(1-.999)/ln(.5) = 9.966 half lives

9.966 * 14.3 = 142.5 days.

Answer 2

28.60 days