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

Mass of original sample = 100 g

Explanation:

Half life of cesium-137 = 30.17 years

Where, k is rate constant

So,  

The rate constant, k = 0.02297 year⁻¹

Time = 90.6 years

Using integrated rate law for first order kinetics as:

Where,  

is the concentration at time t

is the initial concentration

Initial concentration = ?

Final concentration = 12.5 grams

Applying in the above equation, we get that:-

Mass of original sample = 100 g