The half-life of a radioactive sample is $T$. The fraction of the initial mass of the sample that decays in an interval $T / 2$ is

Half-lives for $\alpha$ and $\beta$ emission of a radioactive material are $16$ years and $48$ years respectively. When the material decays by giving $\alpha$ and $\beta$ emission simultaneously,the time in which $3/4$th of the material decays is ....... years.

The half-life of a radioactive nuclide is $100 \, hours$. The fraction of original activity that will remain after $150 \, hours$ would be:

The half-life of a radioactive element $A$ is the same as the mean-life of another radioactive element $B.$ Initially, both substances have the same number of atoms, then

Some nuclei of a radioactive material are undergoing radioactive decay. The time gap between the instances when a quarter of the nuclei have decayed and when half of the nuclei have decayed is given as: (where $\lambda$ is the decay constant)

The radioactivity of a sample is $R_1$ at time $T_1$ and $R_2$ at time $T_2.$ If the half-life of the specimen is $T,$ the number of atoms that have disintegrated in time $(T_2 - T_1)$ is proportional to