Find the mean lifetime of the proton

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Homework Help Overview

The problem involves determining the mean lifetime of a proton based on the decay rate observed in a cubic kilometer of seawater. Participants are exploring the relationship between decay rates and mean lifetime in the context of particle physics.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the number of protons in seawater and the decay rate, questioning how to derive the mean lifetime without knowing the half-life. There is also a focus on the relationship between decay rate and average lifetime.

Discussion Status

Some participants have provided calculations and insights regarding the decay rate and the number of protons, leading to a clearer understanding of how to approach the mean lifetime calculation. However, there is still some uncertainty regarding the correct equations to use.

Contextual Notes

Participants note that the problem specifically asks for the average lifetime rather than the half-life, which influences their approach to the calculations.

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


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) ?
 


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:


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.
 

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