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 acitivity falls to x/20 per ml after 4 half-lives ?a)100 mlb)150 mlc)80 mld)50 ml.Correct answer is option 'D'. Can you explain this answer?

Question

Answer

Solution:

Given, activity per ml of the solution = x
Initial volume of the solution = 200 ml

After 4 half-lives, activity per ml of the solution becomes x/16 (since activity becomes half after each half-life, and after 4 half-lives, the activity becomes (1/2)^4 = 1/16 of the initial activity)

To obtain an activity of x/20 per ml, we need to dilute the solution with water.

Let's assume that we need to add y ml of water to the solution.

So, the final volume of the solution = 200 + y ml

Final activity per ml of the solution = (x/16)/(200 + y)

We want the final activity to be x/20 per ml. So, we can write:

(x/16)/(200 + y) = x/20

Solving for y, we get:

y = 50 ml

Therefore, 50 ml of water should be added to 200 ml of the solution to obtain an activity of x/20 per ml after 4 half-lives.

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