The activity of a radioactive sample is measured as $N_0$ counts per minute at $t = 0$ and $N_0/e$ counts per minute at $t = 5$ minutes. The time (in minutes) at which the activity reduces to half its value is 

A radioactive sample has half-life of $5$ years. Probability of decay in $10$ years will be  ........$\%$

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 ..........$min$

Ther percentage of ${ }^{235} U$ presently on earth is $0.72$ and the rest $(99.28 \%)$ may be taken to be ${ }^{233} U$. Assume that all uranium on earth was produced in a supernova explosion long ago with the initial ratio ${ }^{235} U /^{335} U =2.0$. How long ago did the supernova event occur? (Take the half-lives of ${ }^{235} U$ and ${ }^{238} U$ to be $7.1 \times 10^5$ years and $4.5 \times 10^{9}$ years respectively)

The activity of a sample is $64 × 10^{-5}\, Ci.$ Its half-life is $3\, days$. The activity will become $5 × 10^{-6}\, Ci$ after .........$days$

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