A) \[c\sqrt{\frac{2m}{E}}\]
B) \[\sqrt{\frac{2m}{E}}\]
C) \[\sqrt{\frac{2m}{cE}}\]
D) \[\sqrt{\frac{m}{E}}\]
E) \[\sqrt{\frac{cm}{E}}\]
Correct Answer: A
Solution :
Energy, \[E=\frac{hc}{{{\lambda }_{p}}}\] Or \[{{\lambda }_{p}}=\frac{hc}{E}\] and \[{{\lambda }_{e}}=\frac{h}{p}=\frac{hc}{\sqrt{2mE}}\] \[\therefore \] \[\frac{{{\lambda }_{p}}}{{{\lambda }_{e}}}=\frac{E}{\frac{h}{\sqrt{2mE}}}\] Or \[\frac{{{\lambda }_{p}}}{{{\lambda }_{e}}}=\frac{c\sqrt{2mE}}{E}=c\sqrt{\frac{2m}{E}}\]
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