It is observed that only 25% of a given radioactive sample is left undecayed after 16 days. What is the decay constant of the sample in $day^{-1}$?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 0.087
Given:
$N = 0.25 N_0$
$t = 16\,days$
Radioactive decay law:
$N = N_0 e^{-\lambda t}$
$\frac{N}{N_0} = e^{-\lambda t}$
$0.25 = e^{-16\lambda}$
Taking natural logarithm:
$\ln(0.25) = -16\lambda$
$\lambda = -\frac{\ln(0.25)}{16}$
$\lambda = \frac{\ln(4)}{16}$
$\lambda = \frac{1.3863}{16}$
$\lambda = 0.0866\,day^{-1}$
Final Answer: $\lambda = 0.0866\,day^{-1}$