Define half-life of a radioactive substance. Establish a relation between half-life $t_{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$ and decay constant $\lambda$.

What do you mean by half-life time of a radioactive element? Explain half-life time and decay constant by drawing a curve between undisintegrated atoms of the element and time.

What is meant by the activity of a radioactive substance?

Draw time-activity graph for a radioactive substance. Find the activity after four half-lives in terms of initial activity After how much time the activity will become zero?

What is radioactive decay? Explain decay constant and derive the relation $\frac{N}{N_0}=e^{-\lambda t}$, Also write the meaning of symbols.

The half-life of radium is $1600$ years. What fraction of a sample of radium will be disintegrated after $6400$ years?

The half-life of a radioactive nucleus is $3$ minutes. What fraction of $1 \mathrm{g}$ sample of this element will remain radioactive after $9$ minutes?

The half-life of radon is $3.8$ days. In how many days will its activity drop to $6.25\%$ of its initial value?