1/2 Life Problem

Question

Sodium-24 has a half-life of 15 hours.

How much sodium-24 will remain in a

15.0 g sample after 60 hours?

Answer 1

Certainly the answer given by Mahmud A. is acceptable and correct, but if you run into a problem where the number of half lives that have elapsed is not a whole number (like 4 is in the current problem), then you'll have difficulty. So, here is an easy way to solve these types of problems regardless of the numbers you have.

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

n = # of half lives = 60 hrs/15 hrs = 4

Fraction remaining = 0.5⁴ = 0.0625

0.0625 x 15.0 g = 0.9375 g = 0.938 g (to 3 significant figures)

Answer 2

So to answer this question we have to look at how many half lives passed in the 60 hour period. Since one half life is 15 hours, in 60 hours there are 60/15 = 4 half lives that passed. Meaning in 60 hours we will divide the mass by 2, a total of 4 times.

in half life 1: 15 g / 2 = 7.5g

in half life 2: 7.5g / 2 = 3.75g

in half life 3: 3.75g / 2 = 1.875g

in half life 4 : 1.875g / 2 = 0.9375g

So at the end of 60 hours aka 4 passes of the half life, which leaves us with 0.9375 g of Na-24.

Hope this helped