A) \[{{R}_{1}}{{T}_{1}}-{{R}_{2}}{{T}_{2}}\]
B) \[{{R}_{1}}-{{R}_{2}}\]
C) \[\frac{({{R}_{1}}-{{R}_{2}})}{4}\]
D) \[({{R}_{1}}-{{R}_{2}})\]
Correct Answer: D
Solution :
[d] \[{{T}_{1}}={{N}_{1}}\lambda ,{{R}_{2}}{{N}_{2}}\lambda \] Also \[T=\frac{{{\log }_{e}}2}{\lambda }\] or \[\lambda =\frac{{{\log }_{e}}2}{T}\] \[\therefore {{R}_{1}}-{{R}_{2}}=({{N}_{1}}-{{N}_{2}})\lambda \] \[=({{N}_{1}}-{{N}_{2}})\frac{{{\log }_{e}}2}{T}\] \[\therefore ({{N}_{1}}-{{N}_{2}})=\frac{({{R}_{1}}-{{R}_{2}})T}{{{\log }_{e}}2}\] i.e. \[({{N}_{1}}-{{N}_{2}})\propto ({{R}_{1}}-{{R}_{2}})T\]
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