Question

The fraction of a radioactive material which remains active after time $t$ is $9/16$. The fraction which remains active after time $t/2$ will be

• A. $\frac{4}{5}$
• B. $\frac{7}{8}$
• C. $\frac{3}{5}$
• D. $\frac{3}{4}$

Answer 1

The correct option is D $\frac{3}{4}$

Given : $R/R_o=9/16$ after $t$

Using : $kt=\ln \frac{R_o}{R}$

$\therefore$ $kt=\ln \frac{16}{9}$ ...........(1)

After time $t/2$ :

We get :$k\left(t/2\right)=\ln \frac{R_o}{R}$

$\frac{1}{2}\ln \frac{16}{9}=\ln \frac{R_o}{R}$

$⟹\frac{R}{R_o}=\frac{3}{4}$