A human body required the $$0.01$$  $$M$$ activity of radioactive substance after $$24$$ $$h.$$ Half-life of radioactive substance is $$6h.$$ Then, injection of maximum activity of radioactive substance that can be injected will be

Solution :
$${\text{Remaining activity}} = $$     $$0.01\,M\,\,{\text{after 24 h}}$$
$${\text{Remaining activity}} = $$     $${\text{Initial activity}} \times {\left( {\frac{1}{2}} \right)^n}$$
$$\eqalign{ & {\text{Used half - life time}} \cr & \left( n \right) = \frac{{{\text{Total time}}}}{{{t_{\frac{1}{2}}}}} \cr & \,\,\,\,\,\,\,\,\, = \frac{{24}}{6} \cr & \,\,\,\,\,\,\,\,\, = 4 \cr & {\text{So,}}\,\,\,0.01 = {\text{Initial activity}} \times {\left( {\frac{1}{2}} \right)^4} \cr & {\text{Initial activity}} = 0.01 \times 16 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 0.16 \cr} $$