Mass of Hydrogen needed to determine lifetime of proton

[MxwllsPersuasns]

Homework Statement

The current limit on the proton’s lifetime is determined by observing a large body of water for a long time and noticing that no one of the hydrogen nuclei in H₂O have decayed. Assuming that the experiment making this measurement has been going on for 10 years, how many tons of water are needed to set the constraint on the lifetime of the proton τ > 10³⁴ years?

Homework Equations

N = N₀e^-t/τ

The Attempt at a Solution

For this I would think we would use this equation to then find the amount of protons needed to make -t/τ = -(10)/(10³⁴ and then from that figure out the number of protons in H₂O and then figure out how many molecules then multiply by the molecular weight. Am I on the right track?

 

[mfb]

That will work. You don't even need the full exponential function as the observation time is so tiny compared to the lifetime.

If you expect one decay (at a given lifetime value) and observe no decay, that is not sufficient to rule out this value (you could have been just a bit unlucky), but that is probably a technical detail you don't have to worry about here.