Exponential decay question. fundamental

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SUMMARY

The discussion centers on the exponential decay of muons, which have a mean lifetime of approximately 2 microseconds (μs). Participants clarify that the decay of muons follows an exponential distribution rather than a Gaussian distribution, despite the mean lifetime suggesting a central tendency. The exponential decay plot illustrates the probability of muons remaining over time, confirming that while most will decay, some will persist beyond the mean lifetime. This understanding is rooted in probability theory, emphasizing the distinction between mean values and distribution shapes.

PREREQUISITES
  • Understanding of exponential decay and its mathematical representation.
  • Familiarity with muon properties and behavior in particle physics.
  • Basic knowledge of probability theory and mean lifetime concepts.
  • Ability to interpret graphical data, specifically decay curves.
NEXT STEPS
  • Study the mathematical derivation of exponential decay functions.
  • Explore the concept of mean lifetime in particle physics.
  • Learn about probability distributions, focusing on exponential vs. Gaussian distributions.
  • Investigate real-world applications of exponential decay in various scientific fields.
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Physics students, researchers in particle physics, and anyone interested in understanding decay processes and probability distributions.

rjsbass
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this is just something has been bugging me for the last few days. it seems like it has a very basic solution.

Muons decay randomly, but have a mean lifetime of about 2 us. If I plot the # of muons that decay vs. time (say the axis spans from 0 to 20 us), why is the plot exponential decay? shouldn't it be a gaussian distribution centered around the mean lifetime?
 
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got it. textbooks ftw
 
Last edited:
Suppose you had a pile pile of newly minted muons. After 2 μs, how many would you expect to have left?
 
the majority of them will be gone but some will still remain?
 
You should be able to give a numerical answer from probability theory. Remember, the lifetime is a mean value.
 

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