${ }_{92}^{238} U$ is known to undergo radioactive decay to form ${ }_{82}^{206} Pb$ by emitting alpha and beta particles. A rock initially contained $68 \times 10^{-6} g$ 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 $Z$?

Using a nuclear counter the count rate of emitted particles from a radioactive source is measured. At $t = 0$ it was $1600$ counts per second and $t = 8\, seconds$ it was $100$ counts per second. The count rate observed, as counts per second, at $t = 6\, seconds$ is close to

The half life of a radioactive substance is $20$ minutes. The approximate time interval $(t_2 - t_1)$ between the time $t_2$ when $\frac{2}{3}$ of it had decayed and time $t_1$ when $\frac{1}{3}$ of it had decayed is ..........$min$

The half-life of radon is $3.8\, days$. Three forth of a radon sample decay in  ............$days$

Half life of a radioactive element is $10\, days$. The time during which quantity remains $1/10$ of initial mass will be .........$days$

The half life of a radioactive substance against $\alpha  - $ decay is $1.2 \times 10^7\, s$. What is the decay rate for $4.0 \times 10^{15}$ atoms of the substance