The half-life of a sample of a radioactive substance is $1 \text{ hour}$. If $8 \times 10^{10}$ atoms are present at $t = 0$,then the number of atoms decayed in the duration $t = 2 \text{ hours}$ to $t = 4 \text{ hours}$ will be

The half-life of a radioactive nuclide is $40 \, \text{hours}$. Find the fraction of the substance that has decayed after $20 \, \text{hours}$.

The decay constant of a radioactive element is $1.5 \times 10^{-9} \text{ s}^{-1}$. Its mean life in seconds will be:

$A$ sample contains $10^{-2} \ kg$ each of two substances $A$ and $B$ with half-lives $4 \ s$ and $8 \ s$ respectively. The ratio of their atomic weights is $1:2$. The ratio of the amounts (number of atoms) of $A$ and $B$ remaining after $16 \ s$ is $\frac{x}{100}$. The value of $x$ is:

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

Tritium has a half-life of $12.5\; y$ undergoing beta decay. What fraction of a sample of pure tritium will remain undecayed after $25\; y$?