The half-life of a radioactive substance is $5$ years. What is the probability of decay of this element in $10$ years?

Activity of a radioactive sample is $R_1$ at a time $t_1$ and $R_2$ at a time $t_2$. Its half-life period is $T$. The number of atoms that have disintegrated in the time interval $(t_2 - t_1)$ is equal to $\frac{n(R_1 - R_2)T}{\ln 4}$. Then '$n$' is equal to

$A$ sample of a radioactive element contains $4 \times 10^{16}$ active nuclei. If the half-life of the element is $10$ days,then the number of decayed nuclei after $30$ days is ........ $\times 10^{16}$.

The radioactive materials $x_1$ and $x_2$ have decay constants $10 \lambda$ and $\lambda$ respectively. If initially they have the same number of nuclei,then the ratio of the number of nuclei of $x_1$ to that of $x_2$ will be $1/e$ after a time $t$ equal to:

$A$ radio-isotope has a half-life of $5$ years. The fraction of the atoms of this material that would decay in $15$ years will be

For a radioactive material,the half-life is $10$ minutes. If initially there are $600$ nuclei,the time taken (in minutes) for the disintegration of $450$ nuclei is: