A) \[{{A}_{1}}{{t}_{1}}={{A}_{2}}{{t}_{2}}\]
B) \[{{A}_{1}}-{{A}_{2}}={{t}_{2}}-{{t}_{1}}\]
C) \[{{A}_{2}}={{A}_{1}}{{e}^{({{t}_{1}}-{{t}_{2}})/T}}\]
D) \[{{A}_{2}}={{A}_{1}}{{e}^{({{t}_{1}}/{{t}_{2}})T}}\]
Correct Answer: C
Solution :
\[A={{A}_{0}}{{e}^{-\lambda t}}={{A}_{0}}{{e}^{-t/\tau }};\] where \[\tau =\]mean life So \[\Rightarrow \Delta L=\frac{h}{2\pi }({{n}_{2}}-{{n}_{1}})\]Þ\[{{A}_{0}}=\frac{{{A}_{1}}}{{{e}^{-{{t}_{1}}/T}}}={{A}_{1}}{{e}^{{{t}_{1}}/T}}\] \[\therefore {{A}_{2}}={{A}_{0}}{{e}^{-t/T}}=({{A}_{1}}{{e}^{{{t}_{1}}/T}})\,{{e}^{-{{t}_{2}}/T}}\Rightarrow {{A}_{2}}={{A}_{1}}{{e}^{({{t}_{1}}-{{t}_{2}})/T}}\]
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