Integrated Concepts

Suppose you are designing a proton decay experiment and you can detect 50 percent of the proton decays in a tank of water. (a) How many kilograms of water would you need to see one decay per month, assuming a lifetime of $\text{10}^{\text{31}} \text{y}$? (b) How many cubic meters of water is this? (c) If the actual lifetime is $\text{10}^{\text{33}} \text{y}$, how long would you have to wait on an average to see a single proton decay?