Question

If the half-life of the sample is 5 years and the initial weight of the sample is 64 gm, then the weight remaining after 15 years is:

• A. 16 gm
• B. 32 gm
• C. 8 gm
• D. 4 gm

Hint:

For half-life problems, remember that the remaining amount is halved after each period equal to the half-life.

Answer 1

The Correct Option is C

The formula for half-life decay is: \[ N(t) = N_0 \left( \frac{1}{2} \right)^{\frac{t}{T_{1/2}}} \] where:
- \( N(t) \) is the remaining quantity after time \( t \),
- \( N_0 \) is the initial quantity,
- \( T_{1/2} \) is the half-life of the substance. Given that \( T_{1/2} = 5 \) years and the initial weight is 64 gm, after 15 years: \[ N(15) = 64 \left( \frac{1}{2} \right)^{\frac{15}{5}} = 64 \left( \frac{1}{2} \right)^3 = 64 \times \frac{1}{8} = 8 \, \text{gm}. \] Thus, the remaining weight after 15 years is 8 gm.