$A$ radioactive sample has a half-life of $5 \text{ years}$. The percentage of the fraction decayed in $10 \text{ years}$ will be: (in $\%$)

${ }_{92}^{238} U$ is known to undergo radioactive decay to form ${ }_{82}^{206} Pb$ by emitting alpha and beta particles. $A$ rock initially contained $68 \times 10^{-6} \text{ g}$ of ${ }_{92}^{238} U$. If the number of alpha particles that it would emit during its radioactive decay of ${ }_{92}^{238} U$ to ${ }_{82}^{206} Pb$ in three half-lives is $Z \times 10^{18}$,then what is the value of $Z$?

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

The average life $T$ and the decay constant $\lambda$ of a radioactive nucleus are related as

$A$ 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 .......... $min$.

The activity of a radioactive sample is measured as $N_0$ counts per minute at time $t = 0$ and $N_0/e$ counts per minute at time $t = 3 \text{ minute}$. The time (in minute) in which the activity reduces to half the value, is