The decay constant for the nuclide $^{64}Cu$ is $1.6 \times 10^{-5} \, s^{-1}$. Find the activity of a $1 \, mg$ sample of $^{64}Cu$ in $Ci$. (Given: Atomic mass of Copper = $64 \, g/mol$,$1 \, Ci = 3.7 \times 10^{10} \, Bq$)

$A$ 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; $\log_e 2 = 0.693$]

Plutonium decays with a half-life of $24000 \, \text{years}$. If the plutonium is stored for $72000 \, \text{years}$, then the fraction of plutonium that remains is

$A$ 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 half-life of a radioactive substance is $3.6$ days. How much of $20\, mg$ of this radioactive substance will remain after $36$ days?

Draw a graph of time $t$ versus the number of undecayed nuclei in a radioactive sample and write its characteristics.