Small traces of radioactive substances, mainly from the food we eat, are present in the human body. The most abundant radioisotope in the body is potassium-40. A person weighing 70 kg contains about 150 g of potassium, and about 0.01% of this amount is potassium-40. The half-life of potassium-40 is 1.25 $\times$10⁹ years. Estimate the rate at which radiation is produced by the decay of potassium-40 in the body.

Question

Quizplus · Accepted Answer

The rate of radiation produced by the decay of potassium-40 in the body can be estimated using the formula for radioactive decay, which involves the half-life of the isotope and the amount present in the body. Given that a 70 kg person has about 150 g of potassium, and 0.01% of this is potassium-40, we calculate the amount of potassium-40 as 0.01% of 150 g = 0.015 g. Using the half-life of potassium-40 (1.25 billion years) and converting it into seconds, we can calculate the decay rate. The correct calculation leads to approximately 4,000 decays per second, which is a typical value for the human body's background radiation from potassium-40.

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