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 $day^{-1}$?

0.087

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: $\lambda = 0.0866\,day^{-1}$