Suppose you are designing a proton decay experiment and you can detect 24 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 1031 y?

(b) How many cubic meters of water is this? (Assume the density of water is 1000 kg/m3.)

(c) If the actual lifetime is 1033 y, how long (in months) would you have to wait on an average to see a single proton decay?