A) \[({{A}_{1}}-{{A}_{2}})\]
B) \[\frac{({{A}_{1}}-{{A}_{2}})}{T}\]
C) \[({{A}_{1}}-{{A}_{2}})T\]
D) \[({{A}_{1}}{{t}_{1}}-{{A}_{2}}{{t}_{2}})\]
Correct Answer: C
Solution :
\[{{A}_{1}}={{N}_{1}}\lambda ,\] \[{{A}_{2}}={{N}_{2}}\lambda \] Mean life, \[T=\frac{1}{\lambda }\] \[{{A}_{1}}-{{A}_{2}}=({{N}_{1}}-{{N}_{2}})\lambda \] \[=({{N}_{1}}-{{N}_{2}})\frac{1}{T}\] So, number of atoms disintegrated in\[({{t}_{2}}-{{t}_{1}})s\] \[=({{N}_{1}}-{{N}_{2}})=({{A}_{1}}-{{A}_{2}})T\]
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