The graph between the instantaneous concentration $(N)$ of a radioactive element and time $(t)$ is:

$A$ radioactive substance has decay constants $\lambda_{\alpha}$ and $\lambda_{\beta}$ for $\alpha$ and $\beta$ emission,respectively. If the substance emits both $\alpha$ and $\beta$ particles,find the effective half-life of the substance.

$A$ radioactive sample of half-life $ 10 $ days contains $ 1000x $ nuclei. The number of original nuclei present after $ 5 $ days is: (in $x$)

After two hours, one-sixteenth of the starting amount of a certain radioactive isotope remained undecayed. The half-life of the isotope is:

At some instant,a radioactive sample $S_1$ having an activity $5\,\mu Ci$ has twice the number of nuclei as another sample $S_2$ which has an activity of $10\,\mu Ci$. The half-lives of $S_1$ and $S_2$ are:

If the half-life of radium is $77$ days,its decay constant in $day^{-1}$ will be: