The isotope of uranium with atomic mass 238 decays with a half-life of pi/2 = 4.

Question

The isotope of uranium with atomic mass 238 decays with a half-life of pi/2 = 4.5 x 10 9 years. This means that the number of 238 U atoms surviving after time t out of an original sample of Nq atoms is, on average, N(t) = No2 -t/T1/2. Individual atoms decay at random and are not correlated with one another. (a) What is the probability dP that an individual atom decays in a time dt? Consider a sample of 20 mugm of 238 U. (b) How many 238 U atoms does this sample contain? (c) What is the expected number of decays per second? (d) What is the probability that exactly two decays will be observed in 10 seconds? (e) What is the probability that two or more decays will be observed in 10 seconds?

Explanation / Answer

(a) The probability that a nucleus will decay in the next time interval dt is ?dt = (ln2/T1/2)dt

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