A) \[{{\left( \frac{e}{m} \right)}_{p}}>{{\left( \frac{e}{m} \right)}_{\alpha }}>{{\left( \frac{e}{m} \right)}_{e}}\]
B) \[{{\left( \frac{e}{m} \right)}_{e}}>{{\left( \frac{e}{m} \right)}_{p}}>{{\left( \frac{e}{m} \right)}_{\alpha }}\]
C) \[{{\left( \frac{e}{m} \right)}_{\alpha }}>{{\left( \frac{e}{m} \right)}_{e}}>{{\left( \frac{e}{m} \right)}_{p}}\]
D) none of the above
Correct Answer: B
Solution :
Key Idea: Lighest particle will have highest e/m ratio. The mass of electron \[=9.1\times {{10}^{-31}}\,\text{kg}\] Mass of proton \[=1.67\times {{10}^{-27}}\text{kg}\] Mass of a-particle \[=6.6\times {{10}^{-27}}\,\text{kg}\] Since, \[\frac{e}{m}\] ratio is required, e will be same in case of electron and proton but is 2e for \[\alpha -\]particle. Hence, that ratio will he highest whose mass (m) is lowest irrespective of charge on \[\alpha -\]particle as it does not give greater value to this ratio. As is observed from masses, mass of electron is lowest, therefore e/m ratio of electron is highest. Similarly, \[\alpha -\]particle is heaviest, it will have lowest, \[\frac{e}{m}\]ration
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