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Following statements related to radioactivity are given below: (a) Radioactivity is a random and spontaneous process and is dependent on physical and chemical conditions. (b) The number of un-decayed nuclei in the radioactive sample decays exponentially with time. (c) Slope of the graph of loge (no. of un-decayed nuclei) Vs. time represents the reciprocal of mean life time (τ). (d) Product of decay constant (λ) and half-life time (T1/2) is not constant. Choose the most appropriate answer from the options given below:

1. (a) and (b) only
2. (b) and (d) only
3. (b) and (c) only
4. (c) and (d) only

Correct answer: (b) and (c) only

Solution

Statements (b) and (c) are correct because the decay of un-decayed nuclei follows an exponential decay law, and the slope of the logarithmic graph of un-decayed nuclei versus time indeed represents the reciprocal of the mean lifetime. In contrast, statement (a) is incorrect as radioactivity is not dependent on physical and chemical conditions, and statement (d) is false because the product of the decay constant and half-life is a constant.

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