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Does the number of radioactive nuclei in a sample decrease to exactly half its original value in one half-life? Explain in terms of the statistical nature of radioactive decay.

a) Yes, the decay is precisely exponential.

b) No, decay is statistical, and half-life is an average value.

c) Yes, but only for large samples.

d) No, but the deviation is minimal for short half-lives.

1 Answer

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Final answer:

The number of radioactive nuclei in a sample does not decrease to exactly half its value in one half-life because nuclear decay is a statistical process. While large samples will approximate this behavior, individual nuclei decay based on probabilities, akin to flipping a coin where each has a 50% chance of decaying in one half-life.

Step-by-step explanation:

Does the number of radioactive nuclei in a sample decrease to exactly half its original value in one half-life? In terms of the statistical nature of radioactive decay, the correct answer is b) No, decay is statistical, and half-life is an average value. Half-life is defined as the time taken for half of the radioactive nuclei in a sample to decay. Nuclear decay is a statistical process, meaning that it's based on probabilities, and while in large samples the average behavior will tend to match the expected 50% decay per half-life, it is not a guaranteed outcome for every individual nucleus.

Every nucleus has a 50% chance of decaying during one half-life, analogous to a 50% chance of flipping heads in a coin toss. This probability does not change regardless of how many half-lives have passed. For a sufficiently large number of nuclei, you can expect close to half of the nuclei to have decayed after one half-life, but the behavior of each individual nucleus is random and cannot be predicted precisely.

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