Question

If the half life period of a substance is 5 years, then the total amount of the substance left after 15 years, when initial amount is 64 gms is

• A. 8 gms
• B. 16 gms
• C. 2 gms
• D. 32 gms

Hint:

After \(n\) half-lives, the fraction remaining is \((1/2)^n\). Multiply by the initial amount to get the remaining amount.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
Half-life \(t_{1/2} = 5\) years, initial amount \(N_0 = 64\) g, time \(t = 15\) years. We need the remaining amount.

Step 2: Key Formula or Approach:
For first-order decay, \(N = N_0 \left( \frac{1}{2} \right)^{t / t_{1/2}}\).

Step 3: Detailed Explanation:
Number of half-lives: \(n = \frac{15}{5} = 3\).
Amount remaining: \(N = 64 \times \left( \frac{1}{2} \right)^3 = 64 \times \frac{1}{8} = 8\) g.

Step 4: Final Answer:
Option (A) is correct.