Exponential decay question. fundamental

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Homework Help Overview

The discussion revolves around the concept of exponential decay in the context of muon decay, specifically questioning the nature of the decay plot over time. Participants are exploring the relationship between mean lifetime and the expected distribution of decayed muons.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants question why the decay of muons is represented as an exponential decay rather than a Gaussian distribution. There are inquiries about the expected number of muons remaining after a certain time based on their mean lifetime.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the decay process. Some guidance has been offered regarding the application of probability theory to derive numerical expectations, though no consensus has been reached.

Contextual Notes

Participants are considering the implications of mean lifetime and the randomness of decay, while also addressing the nature of the distribution of remaining muons over time.

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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