An isotope of cesium-137 has a half-life of 30 years. If 5.0 g of cesium-137 decays over 60 years, how many grams will remain? (Please help, thank you!)

Answer 1

@Mona S. gave a perfectly acceptable answer, but I wanted to add the following for when the problem is not as straight forward as the present one. You can use a very simple formula for first order decay...

Fraction Remaining (FR) = 0.5ⁿ where n is the number of half lives that have elapsed.

In the current problem we want to find the FR, and we know n = 2 half lives elapsed (60 yr/30yr = 2)

FR = 0.5² = 0.25

Since we started with 5.0 g, and we have 0.25 (1/4) left, that would be 5.0 g x 0.25 = 1.25 g

Answer 2

Hi Ella,

60 years is 2 half lives because one half life is 30. So after 30 years we would have one half over 5 grams and then after after 30 half of what was remaining. Or we can go 2^2 divided into 5 grams. then do the math.

I hope this helps. Wanted to show you the steps but empower you to do the math and not enable you.

Hope this helps. Let me know if I need to expand on the explanation.