Find the mean lifetime of the proton

[hhhmortal]

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.

Homework Equations

t = 1 / lambda

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 what's the decay rate?

 

[hhhmortal]

How many protons are there in a km^3 of sea water
How many decay per year?
So what's 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 I am 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 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.