If 12.5 grams of the original sample of cesium-137 remained after 90.6 years, what was the mass of the original sample?

2 Answers
Dec 18, 2016

100g

Explanation:

half-life of caesium: 30.2 years

90.6=30.23

remaining mass after 90.6 years = 12.5g
remaining mass after 3 half-lives = 12.5g

1 half-life = original mass 0.51

3 half-lives = original mass 0.53

original mass 0.125 = 12.5g

divide by 0.125:

original mass = (12.50.125)g

=12500125g

=100g

Dec 18, 2016

100gCs

Explanation:

I like to use this equation:

M(t)=M0(12)th

Where the mass of the substance that remains is represented as a function of t, the time which has elapsed in years, and:

M0 is the initial amount of the substance in gram

t is the amount of time which has elapsed

h is the half life of the substance

And in our case (we are solving for the initial amount, M0:

12.5=M0(12)90.630.2

So

M0=12.5(12)90.630.2

and

M0=12.50.125

M0=100