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: Understand half life.
A half life is the time taken for the amount of a substance to fall to half its current value. Here the half life is 5 years and we start with 64 grams.
Step 2: Find how many half lives pass.
The total time is 15 years and each half life is 5 years. So the number of half lives is \[ \frac{15}{5} = 3. \]
Step 3: Halve once.
After the first 5 years the amount halves: $64 \to 32$ grams.
Step 4: Halve again.
After the next 5 years it halves once more: $32 \to 16$ grams.
Step 5: Halve a third time.
After the final 5 years it halves again: $16 \to 8$ grams.
Step 6: Check with the formula.
The general rule is amount left $= 64\times\left(\frac{1}{2}\right)^3 = 64\times\frac{1}{8} = 8$ grams, which agrees. \[ \boxed{8\ \text{grams}} \]