A) \[\frac{1}{c}{{\left( \frac{E}{2m} \right)}^{\frac{1}{2}}}\]
B) \[{{\left( \frac{E}{2m} \right)}^{\frac{1}{2}}}\]
C) \[c\,{{(2mE)}^{\frac{1}{2}}}\]
D) \[\frac{1}{c}{{\left( \frac{2E}{m} \right)}^{\frac{1}{2}}}\]
Correct Answer: A
Solution :
[a] \[{{\lambda }_{e}}=\frac{h}{{{p}_{e}}}=\frac{h}{\sqrt{2\,mE}}\] \[\frac{hc}{{{\lambda }_{P}}}=E\Rightarrow {{\lambda }_{p}}=\frac{hc}{E}\] \[\Rightarrow \,\frac{{{\lambda }_{e}}}{{{\lambda }_{p}}}=\frac{1}{\sqrt{2mE}}\frac{E}{c}=\sqrt{\frac{E}{2m}}\cdot \frac{1}{c}\]
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