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 undecayed nuclei in the radioactive sample decays exponentially with time. (C) Slope of the graph of ( _e( ) no. of undecayed nuclei) vs. time represents the reciprocal of mean life time (( ) ). (D) Product of decay constant (( ) )

Step-by-step solution

Radioactive decay is a random and spontaneous process, it depends on unbalancing of nucleus. This process is dependent on the law of conservation of charge. We know that, (N=N₀ e^ - t (1) ), Where, (N= ) number of decayed nuclei in the sample at time (t ) and (N₀= ) initial number of nuclei. Hence, total number of undecayed nuclei (N₀-N ) Thus, (N₀-N=N₀ (1-e^ - t ) ) This shows that the total number of undecayed nuclei decays exponentially with time. Taking log both sides of equation (1) ( N=- t+ N₀ ) So, slope (=-