Which of the following option is correct? — Nuclear Chemistry and Radioactivity Chemistry Question

💡 Solution & Explanation

Step 1 - The Carbon-14 Cycle $\ce{^{14}C}$ is continuously produced in the upper atmosphere by cosmic-ray neutrons reacting with $\ce{^{14}N}$: $$\ce{^{14}_{7}N + ^{1}_{0}n -> ^{14}_{6}C + ^{1}_{1}H}$$ Once formed, $\ce{^{14}C}$ undergoes radioactive $\beta^-$ decay: $$\ce{^{14}_{6}C -> ^{14}_{7}N + e^- + \bar\nu_e} \quad t_{1/2} = 5770\ \text{yr}$$ Step 2 - Evaluate Each Option **(A)**: "In a living organism, circulation of C-14 from atmosphere is high so that the carbon content is constant." The constant C-14 content in living organisms comes from *equilibrium between intake and decay*, not high circulation. The intake rate equals the decay rate, keeping the ratio $\ce{^{14}C}/\ce{^{12}C}$ constant. → **Incorrect statement.** **(B)**: "Carbon dating can be used to find out the age of earth crust and rocks." Carbon dating is only reliable for organic materials up to ~30,000 years. For geological timescales (billions of years), U-Pb, K-Ar or Rb-Sr dating is used. C-14 half-life (5770 yr) is too short for rock dating. → **Incorrect statement.** **(C)**: "Radioactive absorption due to cosmic radiation is equal to the rate of radioactive decay; hence the carbon content remains constant in living organism." This is the correct description of the **steady-state equilibrium**: the rate of C-14 production by cosmic radiation equals its rate of decay, so the atmospheric (and living-organism) concentration remains constant. → **Correct.** **(D)**: "Carbon dating can be used to determine concentration of C-14 in dead beings." Carbon dating determines the *age* (time since death) by comparing the activity of C-14 in the sample to the known modern value, not the concentration. → **Incorrect statement.** $$\boxed{\text{Answer: C}}$$