What should be the age of fossil for meaningful determination of its age? — Nuclear Chemistry and Radioactivity Chemistry Question

💡 Solution & Explanation

Step 1 - C-14 Dating Range The half-life of $\ce{^{14}C}$ is $t_{1/2} = 5770\ \text{years}$. The passage states: "The method ceases to be accurate over periods longer than 30,000 years." Step 2 - Evaluate Each Option **(A) 6 years**: At 6 years, only $1 - (1/2)^{6/5770} \approx 0.072\%$ of C-14 has decayed. This change in activity is far too small to measure accurately with current instruments. → **Not suitable.** **(B) 6000 years**: About one half-life has elapsed ($6000 \approx 5770$ years). Approximately half the C-14 has decayed, giving a measurable difference in activity that allows accurate age determination. → **Suitable and meaningful.** ✓ **(C) 60,000 years**: About 10 half-lives. Remaining C-14 = $(1/2)^{10} \approx 0.1\%$ of original. Activity is far below the detection threshold; background radiation would mask the signal. → **Too old to date by C-14.** **(D) "It can be used to calculate any age"**: Incorrect. C-14 dating is limited to approximately 30,000 years as stated in the passage. $$\boxed{\text{Answer: B — 6000 years}}$$