How Do You Estimate the Standard Deviation of a Radioactive Counting Rate?

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SUMMARY

The standard deviation of a radioactive counting rate can be estimated using the formula sqrt(N), where N represents the total counts measured. In the discussed scenario, the experimenter recorded 9934 counts, leading to an estimated standard deviation of approximately 100. This conclusion is based on the established statistical principle that the error in counting experiments is derived from the square root of the total counts. Understanding this principle is crucial for accurately interpreting results in radioactive decay experiments.

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  • Understanding of basic statistics, particularly standard deviation and variance.
  • Familiarity with radioactive decay and counting experiments.
  • Knowledge of the square root function and its application in error estimation.
  • Experience with experimental data analysis in physics or related fields.
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  • Study the derivation of the mean and variance in counting distributions.
  • Explore the concept of Poisson distribution as it relates to counting experiments.
  • Learn about error propagation in experimental physics.
  • Review statistical methods for analyzing radioactive decay data.
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Researchers, physicists, and students involved in experimental physics, particularly those working with radioactive materials and data analysis in counting experiments.

quantumworld
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Dear members,
here is a gre problem that I couldn't know how to tackle, any effort will be greatly appreciated.
An experimenter measures 9934 counts during one hour from a radioactive sample. From this number the counting rate of the sample can be estimated with a standard deviation of most nearly
(A) 100
(B) 200
(C) 300
(D) 400
(E) 500
the answer is (A) 100, could anyone please help me out understand this problem :confused:

thanks so much!
 
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the standard deviation in counting experiments is sqrt(N). In this case N is roughly 10000.

p.s. i have no clue why.
 
This one is more or less just remembernig the rules for estimating error.

As you probably guessed, the rule for estimating the error of a count is the square root of the count.

If you're comfortable with statistics, you could probably derive the mean and variance of the "counting" distribution (quotes because I don't remember the right name), use the observed value as an estimate of the mean, and solve for the variance.
 

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