Half life chemistry question

Question

Sodium-24, which is used to locate blood clots in the human circulatory system, has a half-life of 15.0 hours. A sample of sodium-24 with an inital mass of 12.5 g was stored for 45.0 hours. How many grams of sodium-24 is left in the sample after 45.0 hours?

Answer 1

The half-life is defined as the time it takes for half of the original amount to decay. We know in this problem that we started out with an initial amount of 12.5 g and it has been stored for 45.0 hrs. Usually, we can solve for these problems using exponential decay functions. However, a trick to notice here is that 45.0 hrs is exactly 3 times greater than our half-life, 15.0 hrs. That means the material has decreased to half of its amount a total of 3 times:

(1/2)³ = 1/8

In other words, after 45.0 hrs, we will have 1/8 of whatever our initial amount was. Our initial amount was 12.5 g. Thus:

12.5 g * 1/8 = 1.5625 g

There will be 1.5625 g of Sodium-24 remaining after 45.0 hrs.