An 832.8 ng sample of an unknown radioactive substance was placed in storage and its mass

Question

An 832.8 ng sample of an unknown radioactive substance was placed in storage and its mass was measured periodically. After 47 days the amount of radioactive substance had decreased to 104.1 ng. How many half‑lives of the unknown radioactive substance have occurred?

Answer 1

Radioactive decay is a first order reaction, and as such we can use the following relationship for decay and half life:

FR = 0.5ⁿ

FR = fraction remaining

n = # of half lives that have elapsed

FR = 104.1 ng / 832.8 ng = 0.125

This is an easy one, because 0.125 represents 3 half lives.

0.5 = 1 half life

0.25 = 2 half lives

0.125 = 3 half lives

etc.

But to use the original equation, we would have...

0.125 = 0.5ⁿ

log 0.125 = n log 0.5

-0.903 = -0.301 n

n = 3 half lives

Answer 2