The half-life for the radioactive decay of calcium-47 is 4.5 . If a sample has an activity of 3.0 after 27 d , what was the initial activity of the sample?

Question

The half-life for the radioactive decay of calcium-47 is 4.5 . If a sample has an activity of 3.0  after 27 d , what was the initial activity of the sample?

Answer 1

I'll assume the half life is given in days, i.e. 4.5 days, since you didn't give the units.

The simplest way, IMO, to do this is to use the formula FR = 0.5ⁿ where FR = fraction remaining and n is the number of half lives that have elapsed.

n = number of half lives elapsed = 27 d x 1 half life/4.5 days = 6 half lives

FR = 0.5ⁿ = 0.5⁶

FR = 0.015625 = fraction remaining

0.015625 (x) = 3.0

x = 192 = initial activity (no units as no units were given in the original question)