$A$ sample of radioactive material has mass $m$,decay constant $\lambda$,and molar mass $M$. If the Avogadro constant is $N_A$,what is the initial activity of the sample?

$N$ atoms of a radioactive element emit $n$ alpha particles per second. The half-life of the element is:

Half-life of a radioactive element depends upon:

$A$ radioactive substance decays by $10\%$ in $5$ days. What percentage of the original substance will remain after $20$ days (in $\%$)?

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

$A$ piece of bone of an animal from a ruin is found to have $^{14}C$ activity of $12$ disintegrations per minute per gm of its carbon content. The $^{14}C$ activity of a living animal is $16$ disintegrations per minute per gm. How long ago nearly did the animal die? (Given half-life of $^{14}C$ is $t_{1/2} = 5760$ years)