Systematic Error and Data Transformation
To determine the half-life of a radioactive substance, a researcher measures the number of decay events, $N$, over time. The analysis involves plotting $\ln(N)$ versus time to obtain a linear graph. However, the researcher neglects to subtract the constant background radiation from each measurement. What is the primary consequence of this error?
The researcher’s mistake is that they should have plotted N (not its logarithm) versus time to obtain a straight-line relationship.
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 mistake is that plotting versus time is not a valid method for determining half-life in any radioactive decay experiment.
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