Phosphorus-32 has a half life of 2 weeks. After 8 weeks, what percentage of a sample of phosphorus-32 remains undecayed?

Answer 1

A simple formula to use for these types of problems is FR = 0.5ⁿ

FR = fraction remaining

n = number of half lives

In this problem n = 4 half lives (8 weeks x 1 half life/2 weeks = 4 half lives)

So, fraction remaining = 0.5⁴

FR = 0.0625 which is equal to 6.25% remains un-decayed

Answer 2

So in this case, the half life is the amount of time needed for half of the sample to decay.

So, after one half life, 50% of the original sample remains --> after 2 half lives, 25% of the original sample remains --> after 3 half lives, 12.5% remains... and so on and so on.

In this case, 8 weeks is 4 half lives of phosphorus, which translates to 100% at week 0, 50% at week 2, 25% at week 4, 12.5% at week 6, and 6.25% at week 8.