The half-life of radioactive Polonium $(Po)$ is $138.6$ days. For $10^6$ Polonium atoms,the number of disintegrations in $24$ hours is:

$A$ radioactive sample has an average life of $30 \, ms$ and is decaying. $A$ capacitor of capacitance $200 \, \mu F$ is first charged and later connected with a resistor $R$. If the ratio of charge on the capacitor to the activity of the radioactive sample is fixed with respect to time,then the value of $R$ should be $.... \, \Omega$.

The activity of a sample is $64 \times 10^{-5} \, Ci$. Its half-life is $3 \, days$. The activity will become $5 \times 10^{-6} \, Ci$ after ......... $days$.

The activity of a radioactive sample is $9750$ counts/minute at $t = 0$ and $975$ counts/minute at $t = 5$ minutes. The decay constant is .......... $min^{-1}$.

At a certain time,radioactive elements are taken in the ratio $2:1$. Their half-lives are $12$ hours and $16$ hours respectively. What will be the ratio of the undecayed parts after $2$ days?

Obtain the amount of $_{27}^{60} Co$ necessary to provide a radioactive source of $8.0 \; mCi$ strength. The half-life of $_{27}^{60} Co$ is $5.3$ years.