The sample of a radioactive substance has $10^6$ nuclei. Its half-life is $20 \, s$. The number of nuclei that will be left after $10 \, s$ is nearly ...... $\times 10^5$.

$A$ radioactive sample disintegrates via two independent decay processes having half-lives $T_{1/2}^{(1)}$ and $T_{1/2}^{(2)}$ respectively. The effective half-life $T_{1/2}$ of the nuclei is

State and derive the law of radioactive decay.

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?

Half-life of a substance is $10$ years. In what time,it becomes $\frac{1}{4}$ of the initial amount?

$A$ radioisotope $X$ with a half-life of $1.4 \times 10^{9} \text{ years}$ decays into $Y$,which is stable. $A$ sample of rock from a cave was found to contain $X$ and $Y$ in the ratio $1:7$. The age of the rock is ........ $\times 10^{9} \text{ years}$.