Carbon-14 has a half-life of 5730 years. You discover a single carbon-14 nucleus in your laboratory. What is the probability that it will decay in the next 24 hours?

Question

Quizplus · Accepted Answer

We can use the formula for radioactive decay: N=N₀e^(-λt), where N₀ is the initial number of nuclei, N is the remaining number of nuclei, λ is the decay constant (ln2/half-life), and t is the time. We want to find the probability that the nucleus will decay in the next 24 hours, which is the same as finding the probability that the remaining number of nuclei after 24 hours is zero. Thus, we can solve for N/N₀ and use that as the probability.

N/N₀ = e^(-λt) = e^(-0.693/5730 * 24) ≈ 3.3 × 10^-17

Therefore, the probability that the carbon-14 nucleus will decay in the next 24 hours is 3.3 × 10^-17, which is closest to answer choice B.

Carbon-14 Has a Half-Life of 5730 Years