Exponential decay question. fundamental

In summary, the conversation discusses the exponential decay of muons over time, despite their mean lifetime being around 2 us. The individual questioning why the decay is not a gaussian distribution and is provided with a numerical answer from probability theory. They also mention the usefulness of textbooks in understanding this concept.
  • #1
rjsbass
8
0
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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  • #2
got it. textbooks ftw
 
Last edited:
  • #3
Suppose you had a pile pile of newly minted muons. After 2 μs, how many would you expect to have left?
 
  • #4
the majority of them will be gone but some will still remain?
 
  • #5
You should be able to give a numerical answer from probability theory. Remember, the lifetime is a mean value.
 

1. What is exponential decay?

Exponential decay is a mathematical function that describes the decrease of a quantity over time, where the rate of decrease is proportional to the current value of the quantity.

2. What is the formula for exponential decay?

The formula for exponential decay is y = y0 * e-kt, where y is the current value, y0 is the initial value, k is the decay rate, and t is time.

3. How does exponential decay differ from linear decay?

In exponential decay, the rate of decrease is proportional to the current value, while in linear decay, the rate of decrease is constant over time.

4. What are some real-life examples of exponential decay?

Some real-life examples of exponential decay include radioactive decay, population decline, and the decrease in the concentration of a drug in the body over time.

5. How is exponential decay used in science?

Exponential decay is used in many scientific fields, such as physics, chemistry, and biology, to model and predict the behavior of natural phenomena, such as radioactive decay, chemical reactions, and population growth or decline.

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