In a radioactive decay experiment, the starting number of nuclei is 3000. After 1.0 second, it is observed that 1000 ± 40 nuclei have undergone decay. Using the approximation ln(1 + x) ≈ x for |x| << 1, what is the uncertainty Δλ in calculating the decay constant λ (in s⁻¹)?

0.04
0.03
0.02
0.01

Correct answer: 0.02

Solution

The uncertainty Δλ in calculating the decay constant λ is 0.02, which can be determined by applying the approximation ln(1 + x) ≈ x for small x to the equation describing the radioactive decay and then using the given data to calculate the uncertainty.

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