Question

If a radioactive substance is reduced to $6.25%$ of its initial amount in $256$ days then its half-life period is

• A. $126$ days
• B. $64$ days
• C. $50$ days
• D. $25$ days
• E. $12.5$ days

Hint:

Physics Tip: $6.25% = \frac{1}{16}$ instantly tells you four halvings: $100 \to 50 \to 25 \to 12.5 \to 6.25$

Answer 1

The Correct Option is B

Concept:
Radioactive decay law: $$N=N_0\left(\frac12\right)^n$$ where $n$ is number of half-lives elapsed.
Step 1: Convert percentage into fraction.
Given remaining amount: $$6.25%=\frac{6.25}{100}=0.0625=\frac{1}{16}$$ So, $$\frac{N}{N_0}=\frac{1}{16}$$
Step 2: Find number of half-lives.
$$\left(\frac12\right)^n=\frac{1}{16}$$ Since: $$\frac{1}{16}=\left(\frac12\right)^4$$ Therefore: $$n=4$$
Step 3: Find half-life.
Total time = $256$ days $$T_{1/2}=\frac{256}{4}=64\text{ days}$$
Hence correct option is (B). :contentReference[oaicite:0]{index=0}