A) \[{{A}_{1}}\,-\,{{A}_{2}}\]
B) \[{{A}_{1}}{{t}_{1}}\,-\,{{A}_{2}}{{t}_{2}}\]
C) \[\lambda ({{A}_{1}}-{{A}_{2}})\]
D) \[({{A}_{1}}-{{A}_{2}})/\lambda \]
Correct Answer: D
Solution :
According to question, \[{{A}_{1}}=\lambda {{N}_{1}}\,\,at\,\,time\,\,{{t}_{1}}\] \[{{A}_{2}}=\lambda {{N}_{2}}\,\,at\,\,time\,\,{{t}_{2}}\] \[\therefore \] Number of nuclei decayed in interval \[({{t}_{1}}-{{t}_{2}})\] is \[{{N}_{1}}\lambda -{{N}_{2}}\lambda ={{A}_{1}}-{{A}_{2}}\] \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,{{N}_{1}}-{{N}_{2}}=\frac{[{{A}_{1}}-{{A}_{2}}]}{\lambda }\]
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