Answer :
Final answer:
The problem pertains to radioactive decay which follows first-order kinetics. Each radioactive nucleus has a half-life representing the time for the sample to decay by half, and the decay rate can be calculated based on this half-life.
Explanation:
The given problem involves understanding the process of radioactive decay, which applies to radioactive isotopes that change over time. This phenomenon follows first-order kinetics, in which each radioactive nuclide has a characteristic half-life, representing the time required for half the atoms in a sample to decay.
In this case, the radioactive nucleus has a half-life of 2 minutes, and the counting rate is given as 3000 counts per 10 seconds, at time t = 0. Since the decay follows first-order kinetics, it is possible to express the decay constant in terms of the half-life, t1/2.
The decay of unstable radioisotopes is exponential with a half-life of T1/2. It's worth noting that the number of radioactive nuclei reduces rapidly in the first few moments of decay, which is consistent with the radioactive decay law.
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