A radioactive substance is being produced at a constant rate of $10\, nuclei/s.$ The decay constant of the substance is $1/2\, sec^{-1}.$ After what time the number of radioactive nuclei will become $10$ $?$ Initially there are no nuclei present. Assume decay law holds for the sample.

A radioactive nucleus decays by two different processes. The half life for the first process is $10\, s$ and that for the second is $100 s$. the effective half life of the nucleus is close to$.....sec$

The half life of a radioactive substance is $20$ minutes. In $........\,minutes$ time,the activity of substance drops to $\left(\frac{1}{16}\right)^{ th }$ of its initial value.

Radioactivity was discovered by

Two radioactive elements $R$ and $S$ disintegrate as
$R \rightarrow P + \alpha; \lambda_R = 4.5 × 10^{-3} \,\, years^{-1}$
$S \rightarrow P + \beta; \lambda_S = 3 × 10^{-3} \,\, years^{-1}$
Starting with number of atoms of $R$ and $S$ in the ratio of $2 : 1,$ this ratio after the lapse of three half lives of $R$ will be :

$N$ atoms of a radioactive element emit $n$ alpha particles per second. The half life of the element is