# Find the mean lifetime of the proton

## Homework Statement

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.

t = 1 / lambda

## The Attempt at a Solution

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

## Answers and Replies

mgb_phys
Science Advisor
Homework Helper

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

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) ?

mgb_phys
Science Advisor
Homework Helper

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)

Last edited:

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.