$10 \ g$ of a radioactive element is disintegrated to $1 \ g$ in $2.303 \ \text{minutes}$. What is the half-life (in minutes) of that radioactive element?

$A$ radioactive substance is required to have an activity of $0.01 \mu Ci$ in the human body after $24 \ hours$. The half-life of the radioactive substance is $6 \ hours$. What is the maximum initial activity that can be administered (in $\mu Ci$)?

The decay constant of $Ra^{226}$ is $1.37 \times 10^{-11} \ s^{-1}$. $A$ sample of $Ra^{226}$ having an activity of $1.5 \ mCi$ will contain ...... atoms.

The half-life period of a radioactive substance is $8 \ years$. After $16 \ years$,the mass of the substance will reduce from starting $16.0 \ g$ to ....... $g$.

$A$ radioactive substance takes $20 \, \text{min}$ to decay $25 \%$. How many minutes will it take to decay $75 \%$?

$A$ radioactive element gets spilled over the floor of a room. Its half-life period is $30$ days. If the initial activity is ten times the permissible value,after how many days will it be safe to enter the room?