Question

A radioactive material whose half life period is 2 years weighs 1 g and is stored in the laboratory for 4 years. Then the amount of remaining radioactive material is

• A. 0.5 g
• B. 0.125 g
• C. 0.25 g
• D. 0.0625 g

Hint:

The half-life concept implies that after each half-life period, the amount of radioactive material reduces by half. In this case, after 2 years (one half-life), 0.5 g remains. After another 2 years (a total of 4 years, or two half-lives), half of the remaining amount decays, leaving 0.25 g.

Answer 1

The Correct Option is C

Step 1: Identify the given values.
Initial amount of radioactive material, $N_0 = 1$ g
Half-life of the material, $T_{1/2} = 2$ years
Time for which the material is stored, $t = 4$ years

Step 2: Use the formula for radioactive decay.
The amount of radioactive material remaining after time $t$ is given by: $$N(t) = N_0 \left( \frac{1}{2} \right)^{t/T_{1/2}}$$

Step 3: Substitute the given values into the formula.
$$N(4) = 1 \text{ g} \times \left( \frac{1}{2} \right)^{4/2}$$
$$N(4) = 1 \text{ g} \times \left( \frac{1}{2} \right)^{2}$$
$$N(4) = 1 \text{ g} \times \frac{1}{4}$$
$$N(4) = 0.25 \text{ g}$$
Therefore, the amount of remaining radioactive material after 4 years is 0.25 g.