an isotope has half-life of 8 hours. how many grams of a 140 gram sample of this material will remain after 16 hours

Answer 1

More simply.

As the half life is 8 hrs, every 8 hrs we halve the mass left.

So at time 0, we have 140 g

After 8 hrs we have 140 x 0,5 = 70 g

After 8 + 8 hrs (16) we have 70 x 0.5 = 35 g

Answer 2

For problems like this, you could use the integrated rate law for a first order decay, but I find it easier to use the following relationship:

Fraction remaining (FR) = 0.5ⁿ where n = number of half lives that have elapsed

Here, we will solve for FR since we know the half life and the number of half lives elapsed.

n = number of half lives elapsed = 16 hours x 1 half life/8hours = 2 half lives elapsed

FR = 0.5² = 0.25 (this is the fraction that remains)

Grams remaining - 140 g x 0.25 = 35 grams