Question 31.19: The decay constant of a particular isotope is known to be 3....
The decay constant of a particular isotope is known to be 3.0 × 10^{−4} s^{−1}. Determine how long it will take for the activity of a sample of this substance to decrease to one-eighth of its initial value.
Time taken for activity to decrease to \frac{1}{8} of initial value is three half-lives (sequence \frac{1}{2} , \frac{1}{4} , \frac{1}{8}).
Therefore time taken = 3t_{1/2} = 3 \times \frac{0.693}{λ}
=\frac{3 \times 0.693}{3.0 \times 10^{-4}} = 6.96 \times 10^{3} \approx 6900 s
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