How Do You Determine the Decay Constant from a Secondary Graph?

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SUMMARY

The discussion focuses on determining the decay constant, k, for the nuclear decay of 137Ba* using a secondary graph. The key equation involved is 0.693/k = half-life, which relates the decay constant to the half-life of the isotope. Participants suggest creating a linearized graph by taking the natural logarithm (LN) of radiation counts versus time to facilitate the calculation of k. This approach allows for a clearer visualization of the decay process and aids in deriving the lifetime from the fitted equation.

PREREQUISITES
  • Understanding of nuclear decay processes, specifically for isotopes like 137Ba*
  • Familiarity with graphing techniques, particularly linearization of data
  • Knowledge of logarithmic functions, especially natural logarithms (LN)
  • Basic grasp of decay constants and half-life relationships in radioactive decay
NEXT STEPS
  • Study the derivation of the decay constant from half-life equations
  • Learn how to create and interpret linearized graphs in the context of radioactive decay
  • Explore the application of natural logarithms in scientific data analysis
  • Investigate the properties of gamma radiation and its role in nuclear decay processes
USEFUL FOR

This discussion is beneficial for physics students, researchers in nuclear science, and educators looking to enhance their understanding of radioactive decay and graphing methodologies.

Ritzycat
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Homework Statement


Create a secondary graph that allows you to graphically determine the decay constant, k, for the observed nucklear decay of 137Ba*.

Homework Equations


0.693/k = half life
Something with an LN in it

The Attempt at a Solution


I have no idea what it means by "secondary graph". I have absolutely no guidance on what the "secondary graph" is. My first graph was radiation counts vs time, but now it wants this elusive "secondary graph" that will supposedly help me to "graphically determine the decay constant".

I made a linearized graph, if that means anything, by taking LN of the Y axis (radiation counts). I don't see how this helps me though.

Note that in this lab, 137Ba* is decaying to 137Ba through photon emission (gamma radiation)
 

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Ritzycat said:
I made a linearized graph, if that means anything, by taking LN of the Y axis (radiation counts).
I guess this is meant by "secondary graph" (where the "primary graph" was the linear scale).

Ritzycat said:
I don't see how this helps me though.
You have an equation there for your fit. Attach units to it and after some algebra you get your lifetime out of it.
 

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