A radioactive element emits $200$ particles per second. After three hours $25$ particles per second are emitted. The half life period of element will be ……….$minntes$

$90\%$ of a radioactive sample is left undecayed after time $t$ has elapsed. What percentage of the initial sample will decay in a total time $2t$ : …………..$\%$

Radioactive nuclei $P$ and $Q$ disintegrate into $R$ with half lives 1 month and 2 months respectively. At time $t=$ 0 , number of nuclei of each $P$ and $Q$ is $x$. Time at which rate of disintegration of $P$ and $Q$ are equal, number of nuclei of $R$ is …….. $x$

A radioactive nucleus is being produced at a constant rate $\alpha$ per second. Its decay constant is $\lambda $. If $N_0$ are the number of nuclei at time $t = 0$, then maximum number of nuclei possible are

Two radioactive materials $X_1$ and $X_2$ contain same number of nuclei. If $6\,\lambda {s^{ – 1}}$ and $4\,\lambda {s^{ – 1}}$ are the decay constants of $X_1$ and $X_2$ respectively the ratio of number of nuclei, undecayed of $X_1$ to that of $X_2$ will be $\left( {\frac{1}{e}} \right)$ after a time