A) \[\sqrt{\frac{{{m}_{p}}}{{{m}_{e}}}}\]
B) \[\sqrt{\frac{{{m}_{e}}}{{{m}_{p}}}}\]
C) \[\frac{1}{2}\sqrt{\frac{{{m}_{e}}}{{{m}_{p}}}}\]
D) \[2\sqrt{\frac{{{m}_{e}}}{{{m}_{p}}}}\]
Correct Answer: D
Solution :
[d] Energy in joule (E)= charge \[\times \] potential diff. in volt. \[{{E}_{electron}}={{q}_{e}}V\text{ and }{{\text{E}}_{proton}}={{q}_{p}}4V\] De-Broglie wavelength \[{{\lambda }_{e}}=\frac{h}{\sqrt{2{{m}_{e}}eV}}\text{and }{{\lambda }_{p}}=\frac{h}{\sqrt{2{{m}_{p}}e4V}}\] \[(\therefore {{q}_{e}}={{q}_{p}})\] \[\therefore \frac{{{\lambda }_{e}}}{{{\lambda }_{p}}}=\frac{\frac{h}{\sqrt{2{{m}_{e}}eV}}}{\frac{h}{\sqrt{2{{m}_{p}}e4V}}}=\sqrt{\frac{2{{m}_{p}}e4V}{2{{m}_{e}}eV}}=2\sqrt{\frac{{{m}_{p}}}{{{m}_{e}}}}\]You need to login to perform this action.
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