A) \[{{l}_{1}}{{t}_{2}}-{{l}_{2}}{{t}_{1}}\]
B) \[{{l}_{1}}-{{l}_{2}}\]
C) \[\frac{{{l}_{1}}-{{l}_{2}}}{{{\tau }_{1/2}}}\]
D) \[\left( {{l}_{1}}-{{l}_{2}} \right)\,{{\tau }_{1/2}}\]
Correct Answer: D
Solution :
Half-life \[{{\tau }_{1/2}}\,\,=\,\,\frac{0.693}{\lambda }\] Activity \[{{I}_{1}}\,\,=\,\,\lambda {{N}_{1}},\,\,and\,\,{{I}_{2}}\,\,=\,\,\lambda {{N}_{2}}\] \[\lambda \,\,\to \,\, disintegration constant\] \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,{{l}_{1}}-{{l}_{2}}=({{N}_{1}}-{{N}_{2}})\frac{0.693}{{{\tau }_{1/2}}}\] \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,({{N}_{1}}-{{N}_{2}})\,\,\propto \,\,({{l}_{1}}-{{l}_{2}})\,{{\tau }_{1/2}}\]You need to login to perform this action.
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