A) \[{{\lambda }_{e}}>{{\lambda }_{p}}\]
B) \[{{\lambda }_{p}}>{{\lambda }_{\alpha }}\]
C) \[{{\lambda }_{e}}>{{\lambda }_{\alpha }}\]
D) \[{{\lambda }_{\alpha }}<{{\lambda }_{p}}<{{\lambda }_{e}}\]
Correct Answer: A
Solution :
de-Broglie wavelength \[\lambda =\frac{h}{mv}\] or \[\lambda \propto \frac{1}{m}\] \[\therefore \] \[{{\lambda }_{e}}\propto \frac{1}{{{m}_{e}}},\,{{\lambda }_{\alpha }}\propto \frac{1}{{{m}_{\alpha }}}\] and \[{{\lambda }_{p}}\propto \frac{1}{{{m}_{p}}}\] As we know that \[{{m}_{e}}<{{m}_{p}}<{{m}_{a}}\] So, \[{{\lambda }_{e}}>{{\lambda }_{p}}>{{\lambda }_{\alpha }}\] or \[{{\lambda }_{e}}>{{\lambda }_{\alpha }}\] or \[{{\lambda }_{p}}>{{\lambda }_{\alpha }}\] or \[{{\lambda }_{e}}>{{\lambda }_{p}}\]
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