A radioactive element ${ }_{92}^{242} X$ emits two $\alpha$-particles, one electron and two positrons. The product nucleus is represented by ${ }_{ P }^{234} Y$. The value of $P$ is $..................$

In saloons, there is always a characteristics smell due to the ammonia-based chemicals used in hair dyes and other products. Assume the initial concentration of ammonia molecules to be $1000 \,molecules/ m ^3$. Due to air ventilation, the number of molecules leaving in one minute is one tenth of the molecules present at the start of that minute. How long will it take for the concentration of ammonia molecules to reach $1 \,molecule / m ^3$ ?

Starting with a sample of pure $^{66}Cu,\,\frac{7}{8}$ of it decays into $Zn$ in $15\, min$. The corresponding half-life is .......... $min$

Two radioactive samples $A$ and $B$ have half lives $T_1$ and $T_2\left(T_1 > T_2\right)$ respectively At $t=0$, the activity of $B$ was twice the activity of $A$. Their activity will become equal after a time

Why radioactivity is considered a nuclear phenomenon ?

A radioactive nucleus $A$ with a half life $T$, decays into a nucleus $B.$ At $t = 0$, there is no nucleus $B$. At sometime $t$, the ratio of the number of $B$ to that of $A$ is $0.3$. Then, $t$ is given by