$A$ radioactive element emits $200$ particles per second. After $3$ hours,$25$ particles per second are emitted. The half-life period of the element will be .......... $minutes$.

The half-life of $Bi^{210}$ is $5$ days. If we start with $50,000$ atoms of this isotope,the number of atoms left over after $10$ days is:

The half-life of a radioactive element is $10 \, days$. The time required for the mass of the sample to reduce to $\frac{1}{10}$ of its initial mass is approximately ........ days.

$A$ radioactive nucleus $A$ has a single decay mode with half-life $\tau_A$. Another radioactive nucleus $B$ has two decay modes $1$ and $2$. If decay mode $2$ were absent,the half-life of $B$ would have been $\tau_A / 2$. If decay mode $1$ were absent,the half-life of $B$ would have been $3 \tau_A$. If the actual half-life of $B$ is $\tau_B$,then the ratio $\tau_B / \tau_A$ is

$A$ radioactive element having a half-life of $30 \ min$ is undergoing beta decay. The fraction of the radioactive element that remains undecayed after $90 \ min$ will be:

If $T$ is the half-life of a radioactive material,then the fraction that would remain after a time $\frac{T}{2}$ is