# Find the mean lifetime of the proton

by hhhmortal
 P: 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?
 Sci Advisor HW Helper P: 8,953 How many protons are there in a km^3 of sea water How many decay per year? So whats the decay rate?
P: 176
 Quote by mgb_phys How many protons are there in a km^3 of sea water How many decay per year? So whats the decay rate?
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) ?

 Sci Advisor HW Helper P: 8,953 Find the mean lifetime of the proton It doesn't ask for a halflife it asks for an average lifetime. 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)
P: 176
 Quote by mgb_phys It doesn't ask for a halflife it asks for an average lifetime. 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)
It makes sense now, thanks! I calculated the mean lifetime to be 2 x 10^29 years, which looks about right.

 Related Discussions Advanced Physics Homework 3 Introductory Physics Homework 8 High Energy, Nuclear, Particle Physics 23 Introductory Physics Homework 1