The half-life of sodium 24 is 15.7 hours. How long will it take for 68.1% of a 5.5 μg sample to decay?

Question

This is a first order process. Report answer in hours to two decimals.

Answer 1

There are different equations that can be used for this type of problem, but I find the easiest is the following:

Fraction remaining = 0.5ⁿ where n is the number of half lives that have elapsed

In this problem, we are given

half life = 15.7 hrs

fraction remaining = 100% - 68.1% = 31.9% = 0.319 as a fraction

We now solve for n, the number of half lives elapsed

0.319 = 0.5ⁿ

log 0.319 = n log 0.5

-0.496 = -0.301n

n = 1.65 half lives

Converting this to hours, we have...

1.65 half lives x 15.7 hrs/half life = 25.0 hours