Read Decay Data: Extract Half-Life and Its Error
Exponential decay becomes a straight calculation after taking a logarithm. Measurement uncertainty must be propagated through that logarithm, not added directly to time.
Half-Life from Measured Decay Counts is the central idea in this question pattern. Identify the condition in the stem before applying the method below.
Start with the condition
For small fractional count uncertainty, use δ ln N approximately ΔN/N.
Build the governing relation
The initial count is exact in this setup, so the stated uncertainty belongs to the later measured count.
Finish with a physical check
Check the limiting case before selecting an option: remove the special feature in the diagram or make the relevant parameter very large or very small. The result should reduce to a familiar relation.
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- ✓State the physical condition before choosing a formula.
- ✓Keep direction, sign and constraint information explicit.
- ✓Test one limiting case before committing to an option.
Treating the uncertainty in N as an equal percentage uncertainty in half-life without differentiating reverses the dependence.
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