The activity of a radioactive sample falls from $700 \;\mathrm{s}^{-1}$ to $500\; \mathrm{s}^{-1}$ in $30\;min$. Its half life is close to………$min$

A radioactive nucleus is being produced at a constant rate $\alpha$ per second. Its decay constant is $\lambda $. If $N_0$ are the number of nuclei at time $t = 0$, then maximum number of nuclei possible are

Half-life of a radioactive substance is $20$ minutes. Difference between points of time when it is $33\%$ disintegrated and $67\%$ disintegrated is approximately ……….. $min$

Which of the following statements are true regarding radioactivity

$(I)$ All radioactive elements decay exponentially with time

$(II)$ Half life time of a radioactive element is time required for one half of the radioactive atoms to disintegrate

$(III)$ Age of earth can be determined with the help of radioactive dating

$(IV)$ Half life time of a radioactive element is $50\%$ of its average life periodSelect correct answer using the codes given belowCodes :

The radioactivity of a given sample of whisky due to tritium (half life $12.3$ years) was found to be only $3\%$ of that measured in a recently purchased bottle marked $"7$ years old". The sample must have been prepared about