chemistry radioactive decay

Question

The radioactive isotope ²³⁴Th has a half-life of 24.1 days. If a sample contains 40.7 mg of ²³⁴Th, what mass of the isotope will remain after 38.6 days?

Answer 1

First, find out how many half lives have elapsed.

38.6 days/ 24.1 days = 1.60 half lives

Next you can use the formula F = 0.5ⁿ where

F = fraction remaining =?

n = number of half lives elapsed = 1.60

F = 0.5^1.60

F = 0.330 which means that 33% remains

mass remaining = 40.7 mg x 0.33 = 13.4 mg