# Find the mean lifetime of the proton

1. ### hhhmortal

176
1. The problem statement, all variables and given/known data

Three proton decays per cubic kilometer of water per year are detected by an array of photomultipliers immersed in the sea. Find the mean lifetime of the proton.

2. Relevant equations

t = 1 / lambda

3. The attempt at a solution

How is it possible to work this out without knowing the halflife?

2. ### mgb_phys

8,952

How many protons are there in a km^3 of sea water
How many decay per year?
So whats the decay rate?

3. ### hhhmortal

176

Well I calculated the amount of protons per km^3 using moles and grams and it is
about 6 x 10^29 , but im not too sure if this is correct.

the decay rate is 3 proton per km^3 per year but what equation do I need to work out the mean halflife?

is it decay rate = (lambda)(N)e^-(lambda)(t) ?

4. ### mgb_phys

8,952

If 3 in 6 x 10^29 decay per year - then the average time for a proton to decay is just 1/decay rate (from dimensions)

Last edited: May 14, 2009
5. ### hhhmortal

176

It makes sense now, thanks! I calculated the mean lifetime to be 2 x 10^29 years, which looks about right.