Question

A radioactive substance was reduced to $\frac{1}{4}$th of the original amount in 8 days. The time taken by the same radioactive substance to get reduced to $\frac{1}{8}$th of the remaining amount is _____________.

• A. 12 days
• B. 16 days
• C. 20 days
• D. 8 days

Answer 1

The correct option is A 12 days

$\ln \frac{A_t}{A_o}=-kt\left(1\right)\ln \frac{1}{4}=-k\times 8k=\frac{\ln 4}{8}$

So, $\ln \frac{1}{8}=\frac{-\ln 4}{8}t\ln 8=\frac{\ln 4}{8}t\Rightarrow 3\ln 2=\frac{2\ln 2}{8}tt=12days$