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)?

At a given instant,say $t = 0$,two radioactive substances $A$ and $B$ have equal activities. The ratio $\frac{R_B}{R_A}$ of their activities after time $t$ decays with time $t$ as $e^{-3t}$. If the half-life of $A$ is $\ln 2$,the half-life of $B$ is:

$A$ radioactive element $X$ converts into another stable element $Y$. The half-life of $X$ is $2 \text{ hours}$. Initially,only $X$ is present. After a time $t$,if the ratio of atoms of $X$ to $Y$ is $1:4$,then the value of $t$ is

$A$ radioactive element decays to form a stable nuclide. The graph representing the number of radioactive nuclei $(N)$ versus time $(t)$ is:

The radioactivity of a certain radioactive element drops to $1/64$ of its initial value in $30 \, s$. Its half-life is ......... $s$.

$A$ radioactive isotope $X$ has a half-life of $20$ years and decays into a stable element $Y$. In a given rock sample, the ratio of the amounts of $X$ and $Y$ is found to be $1:7$. The estimated age of the rock is ......... years.