Question

Activity of a radioactive sample decreases to $\left(\dfrac{1}{4}\right)^{th}$ of its original value in 4 days. Then in 16 days its activity will become $x$ times the original value. The value of $x$ is

• A. $\dfrac{1}{16}$
• B. $\dfrac{1}{32}$
• C. $\dfrac{1}{256}$
• D. $\dfrac{1}{128}$

Hint:

Activity falling to a quarter takes two half-lives.

Answer 1

The Correct Option is C

Step 1: Approach
Use repeated quartering.

Step 2: Every 4 days
Activity is multiplied by $\dfrac14$ every 4 days. In 16 days there are 4 such periods.

Step 3: Result
$\left(\dfrac14\right)^4=\dfrac1{256}$. Option (C).

Final Answer:
Activity quarters every 4 days, so in 16 days it becomes 1/256 of the original, option (C). \[ \boxed{\frac{1}{256}} \]