question_answer

A radioactive substance decays to \[1/32\]th of its initial activity in 25 days. Calculate its half life.                                    

Answer:

                Here\[R={{R}_{0}}/16\]                 But \[R={{R}_{0}}{{\left( \frac{1}{2} \right)}^{n}}\]                 \[\therefore \]  \[\frac{{{R}_{0}}}{32}={{R}_{0}}{{\left( \frac{1}{2} \right)}^{n}}\] or \[{{\left( \frac{1}{2} \right)}^{5}}={{\left( \frac{1}{2} \right)}^{n}}\]                 or            \[n=5\] Half-life period \[\text{=}\frac{\text{Time of distegration}}{\text{No}\text{.of half-lives}}\text{=}\frac{\text{25}}{\text{5}}\text{= }\mathbf{5days}\]