The fraction $f$ of radioactive material that has decayed in time $t$,varies with time $t$. The correct variation is given by the curve

$A$ sample of living carbon-containing matter has an activity of $15$ decays/minute per gram of carbon-$14$. $A$ sample from the Indus Valley civilization has an activity of $9$ decays/minute per gram of carbon-$14$. Given the half-life of $C^{14}$ is $5730$ years, find the age of the Indus Valley civilization.

At a given instant,a radioactive sample has $N$ active nuclei. If its decay constant is $\lambda$,which of the following relations is incorrect? (Note: $\lambda$ is very small.)

The activity of a freshly prepared radioactive sample is $10^{10}$ disintegrations per second,whose mean life is $10^9 \ s$. The mass of an atom of this radioisotope is $10^{-25} \ kg$. The mass (in $mg$) of the radioactive sample is

The radioactive sources $A$ and $B$ have half-lives of $2 \ hr$ and $4 \ hr$ respectively,and initially contain the same number of radioactive atoms. At the end of $2 \ hr$,their rates of disintegration are in the ratio:

For a substance,the average life for $\alpha$-emission is $1620$ years and for $\beta$-emission is $405$ years. After how much time will $1/4$ of the material remain after both $\alpha$ and $\beta$ emissions?