The half-life of radioactive $Po$ (Polonium) is $138.6 \, \text{days}$. For $1,000,000$ Polonium atoms, the number of disintegrations in $24 \, \text{hours}$ is:

Half-lives of two radioactive substances $A$ and $B$ are,respectively,$20 \ min$ and $40 \ min$. Initially,the samples of $A$ and $B$ have an equal number of nuclei. After $80 \ min$,the ratio of the remaining number of $A$ and $B$ nuclei is

$A$ count rate meter shows a count of $240$ per minute from a given radioactive source. One hour later,the meter shows a count rate of $30$ per minute. The half-life of the source is .......... $min$.

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?

After $280$ days,the activity of a radioactive sample is $6000 \, dps$. The activity reduces to $3000 \, dps$ after another $140$ days. The initial activity of the sample in $dps$ is

An element used for radioactive carbon dating for more than $5600$ years is