The mean life of a radioactive material for alpha decay and beta decay are,respectively,$1620$ years and $520$ years. What is the half life of the sample (in years)?

The decay constant of radium is $4.28 \times 10^{-4}$ per year. Its half-life will be .......... $years$.

Element $X$ decays into element $Y$ with a half-life of $3$ days. On March $1$st,the mass of $X$ is $10 \, g$. What will be the masses of $X$ and $Y$ after $6$ days?

$A$ radioactive substance is being produced at a constant rate of $10 \text{ nuclei/s}$. The decay constant of the substance is $0.5 \text{ s}^{-1}$. After what time will the number of radioactive nuclei become $10$? Initially,there are no nuclei present. Assume the decay law holds for the sample.

$A$ radioactive substance decays to $\left(\frac{1}{16}\right)^{th}$ of its initial activity in $80\, days$. The half-life of the radioactive substance expressed in days is ... .

$A$ sample initially contains only $U-238$ isotope of uranium. With time,some of the $U-238$ radioactively decays into $Pb-206$ while the rest of it remains undisintegrated. When the age of the sample is $P \times 10^8$ years,the ratio of the mass of $Pb-206$ to that of $U-238$ in the sample is found to be $7$. The value of $P$ is. . . . . . [Given: Half-life of $U-238$ is $4.5 \times 10^9$ years; $\log_e 2 = 0.693$]