Find the mean lifetime of the proton

In summary, an array of photomultipliers in the sea has detected three proton decays per cubic kilometer of water per year. By using the equation t = 1/lambda, the mean lifetime of the proton can be calculated. The number of protons in a cubic kilometer of sea water was found to be approximately 6 x 10^29, with a decay rate of 3 proton per km^3 per year. The mean lifetime of a proton was then calculated to be 2 x 10^29 years.
  • #1
hhhmortal
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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?
 
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  • #2


How many protons are there in a km^3 of sea water
How many decay per year?
So what's the decay rate?
 
  • #3


mgb_phys said:
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) ?
 
  • #4


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:
  • #5


mgb_phys said:
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.
 

1. What is the mean lifetime of the proton?

The mean lifetime of the proton is the average time it takes for a proton to decay. It is currently estimated to be around 10^34 years.

2. How is the mean lifetime of the proton determined?

The mean lifetime of the proton is determined through experiments and calculations based on the behavior of protons in various environments.

3. Why is it important to know the mean lifetime of the proton?

Knowing the mean lifetime of the proton can provide valuable insights into the fundamental properties of matter and the stability of the universe.

4. Has the mean lifetime of the proton changed over time?

There is currently no evidence to suggest that the mean lifetime of the proton has changed over time. However, further research and experiments are needed to confirm this.

5. Can the mean lifetime of the proton be extended or shortened?

At this time, the mean lifetime of the proton is considered to be a fundamental constant and cannot be altered. However, new discoveries in particle physics may one day lead to changes in this understanding.

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