A) \[{{R}_{1}}{{T}_{1}}-{{R}_{2}}{{T}_{2}}\]
B) \[{{R}_{1}}-{{R}_{2}}\]
C) \[\frac{{{R}_{1}}-{{R}_{2}}}{T}\]
D) \[({{R}_{1}}-{{R}_{2}})T\]
Correct Answer: D
Solution :
\[{{R}_{1}}={{N}_{1}}\lambda \]and\[{{R}_{2}}={{N}_{2}}\lambda \] Also \[T=\frac{{{\log }_{e}}2}{\lambda }\] Or \[\lambda =\frac{{{\log }_{e}}2}{T}\] \[\therefore \] \[{{R}_{1}}-{{R}_{2}}=({{N}_{1}}-{{N}_{2}})\lambda \] \[=({{N}_{1}}-{{N}_{2}})\frac{{{\log }_{e}}2}{T}\] \[\therefore \] \[({{N}_{1}}-{{N}_{2}})=\frac{({{R}_{1}}-{{R}_{2}})T}{{{\log }_{e}}2}\] ie, \[({{N}_{1}}-{{N}_{2}})\propto ({{R}_{1}}-{{R}_{2}})T\]You need to login to perform this action.
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