Question

The half life of a radioactive substance is 20 minutes. In how much time the activity of substance drops to $(\frac{1}{16})^{th}$ of its initial value?

• A. 80 minutes
• B. 20 minutes
• C. 40 minutes
• D. 60 minutes

Answer 1

Answer: (A)

80 minutes

Answer 2

The correct option is (A): 80 minutes

Left fraction of activity = $\frac{1}{16}$

$\frac{R}{R_0}=(\frac{1}{2})^{\frac{t}{2}}$

$\frac{1}{16}=(\frac{1}{2})^{\frac{t}{2}}$

$(\frac{1}{2})^4=(\frac{1}{2})^{\frac{t}{2}}$

4=\frac{t}{20}$$\Rightarrow$$t=80