• # question_answer The half-life period of a radioactive element X is same as the mean-life time of another radioactive element Y. Initially both of them have the same number of atoms. Then A) X and Y have the same decay rate initiallyB) X and Y decay at the same rate alwaysC) Y will decay at a faster rate than XD) X will decay at a faster rate than Y

$\frac{0.693}{{{\lambda }_{X}}}=\frac{1}{{{\lambda }_{Y}}}$or ${{\lambda }_{Y}}>{{\lambda }_{X}}$ Activity $=A=\lambda N\Rightarrow A\propto \lambda \Rightarrow {{A}_{y}}>{{A}_{x}}$ As activity of Y is greater so, Y will decay faster than X. Hence, the correction option is (c).