Given that a radioactive species decays according to the exponential law $N = N_0 e^{-\lambda t}$,the half-life of the species is:

The $t_{1/2}$ of a radioactive element is $20 \ min$. The time interval between the stages of its $33\%$ and $67\%$ decay is ....... $min$.

$A$ 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 $\mu Ci$)?

Gadolinium-$153$,which is used to detect osteoporosis (porous bones),has a half-life of $242$ days. Which value is closest to the percentage of $Gd-153$ left in a patient's system after $2$ years? .......... $\%$

$A$ radioactive substance has a half-life $(t_{1/2})$ of $60 \ minutes$. After $3 \ hours$,what percentage of the radioactive substance will remain?

For a radioactive substance with a half-life period of $500$ years,the time required for the complete decay of $100 \ mg$ of it would be: