Question

The activity per ml of a solution of radioactive substance is x. How much water be added to 200 ml of this solution so that the activity falls to x/20 per ml after 4 half-lives?

• A. 100 ml
• B. 150 ml
• C. 80 ml
• D. 50 ml

Answer 1

Answer: (D)

50 ml

The initial activity is $x\times 200$.
Let V ml be the volume of the solution. The activity after four half-lives is $=\frac{x}{20}\times V.$

$N=N_0{\left(\frac{1}{2}\right)}^n$

$\left(\frac{xV}{20}\right)=(x\times 200){\left(\frac{1}{2}\right)}^4$

Thus the final volume is 250 ml.
Hence, 50 ml of water is added.

Hence, option D is correct.