Given data

• Half-life, $t_{1/2} = 3$ hours
• Initial mass, $N_0 = 256\,\text{g}$
• Total time elapsed, $t = 18$ hours

Find the number of half-lives elapsed $n = \frac{t}{t_{1/2}} = \frac{18}{3} = 6$

Use the radioactive decay formula After $n$ half-lives, the remaining mass is: $N = N_0\left(\frac{1}{2}\right)^n$

Substituting the values: $N = 256\left(\frac{1}{2}\right)^6$

Calculate $\left(\frac{1}{2}\right)^6 = \frac{1}{64}$ So, $N = 256 \times \frac{1}{64} = 4\,\text{g}$

Match with the options

• A: $8.0\,\text{g}$
• B: $12.0\,\text{g}$
• C: $16.0\,\text{g}$
• D: $4.0\,\text{g}$

Therefore, the correct option is D.

Comparison with stored correct answer Stored correct answer: D

My derived answer also gives D. So they agree.