What is the Mean Lifetime of Muons?

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SUMMARY

The mean lifetime of muons can be determined using the decay equation y(t)=Ne^(-t/τ), where τ represents the mean lifetime and N is the initial number of muons. In the discussion, a histogram was created to visualize muon decay, but the user struggled to extract the mean lifetime from the data. The correct approach involves plotting the natural logarithm of the decay rate, dy/dt, to find the decay constant, which is the inverse of the mean lifetime. This method provides a clear path to calculating the mean lifetime accurately.

PREREQUISITES
  • Understanding of exponential decay and its mathematical representation.
  • Familiarity with histogram data representation.
  • Proficiency in using Excel for data analysis and trendline fitting.
  • Knowledge of natural logarithms and their application in decay equations.
NEXT STEPS
  • Learn how to plot natural logarithms of decay rates in Excel.
  • Study the relationship between decay constants and mean lifetimes in particle physics.
  • Explore advanced data fitting techniques for analyzing experimental data.
  • Investigate the concept of activity in radioactive decay and its implications.
USEFUL FOR

Students in physics, particularly those conducting experiments in particle physics, as well as educators and researchers interested in muon decay and statistical data analysis.

FlixB
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Homework Statement


I am doing an experiment where I try to the determine the mean lifetime of muons. I collected enough data and I put it in a histogram (attached file), but I have no idea how to calculate the mean lifetime with this.

Homework Equations


y(t)=Ne^(-t/τ), where τ is the mean lifetime and N the initial amount of muons

The Attempt at a Solution


I plotted a trendline in excel and got a line with the formula y=-4.85ln(x)+10.637, which wasn't very helpful.
Because the histogram shows the amount of muons that decays and not the amount of muons left I thought I should use dy/dt=Ne^(-t/τ)*(-1/τ), but this hasn't gotten me any closer either.
 

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Hello Flix, welcome to PF :smile:

This fitted line has a slope for ln(y) . Did you check what you expect for the slope of the line obtained when plotting ln(dy/dt) ?
 
The counts is in effect the activity, A, of the sample.
The mean life of the muons is the inverse of the decay constant.
 

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