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Answer :
Final answer:
The half-life of the isotope is approximately 36.5 hours.
Explanation:
The half-life of an isotope is the time it takes for half of the radioactive nuclei in a sample to decay. To find the half-life, we can use the formula
t1/2 = ln(2) / λ
Given that the isotope decays to 6.25% of its original activity in 36.6 hours, we can calculate the decay constant λ using the equation
0.0625 = e-λ(36.6)
Solving for λ, we find that λ ≈ 0.019/h. Substituting this value into the half-life formula, we get:
t1/2 = ln(2) / 0.019 ≈ 36.5 hours.
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