APFIVE Experimental Procedure: A researcher studying radioactive decay measures the number of decay events over time. The researcher plots $$\ln(N)$$ versus time to determine the half-life of the substance. However, the researcher neglects to subtract the background radiation counts from the recorded values, causing the entire dataset to be shifted. What is the mistake?
The mistake is that plotting $$\ln(N)$$ versus time is not a valid method for determining half-life in any radioactive decay experiment.
The error arises because the natural logarithm was applied instead of the common logarithm, which is required in half-life calculations.
The researcher failed to subtract the background radiation, which introduces systematic error into the logarithmic plot and leads to inaccurate determination of the half-life.
The researcher’s mistake is that they should have plotted N (not its logarithm) versus time to obtain a straight-line relationship.
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