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------------------------------------------------ Suppose a radioactive nucleus has a half-life of 2 minutes, and the counting rate at [tex]t = 0[/tex] is 3000 counts/s. What is the counting rate after 2 minutes?

The counting rate of a radioactive substance, which has a half-life of 2 minutes, will reduce to half its initial rate after two minutes. Thus, the counting rate drops from 3000 counts/s to 1500 counts/s.

Explanation:

The radioactive decay of a substance can be calculated using the concept of half-life, which in this question is given as 2 minutes. A half-life is the time taken for half of the radioactive atoms in a sample to decay. Thus, if a radioactive sample has a half-life of 2 minutes, this means that half of its atoms will decay every 2 minutes.

So, in 2 minutes (which is one half-life), the counting rate of 3000 counts/s will reduce to half. Therefore, the counting rate after 2 minutes would be 1500 counts/s.

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