Radioactivity.

hhhmortal

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?

mgb_phys

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

hhhmortal

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

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)

hhhmortal

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