A) \[\frac{1}{c}{{\left( \frac{E}{2m} \right)}^{\frac{1}{2}}}\]
B) \[{{\left( \frac{E}{2m} \right)}^{\frac{1}{2}}}\]
C) \[c{{\left( 2mE \right)}^{\frac{1}{2}}}\]
D) \[\frac{1}{xc}{{\left( \frac{2m}{E} \right)}^{\frac{1}{2}}}\] (c being velocity of light)
Correct Answer: A
Solution :
| [a] For electron \[\,{{\lambda }_{e}}=\frac{h}{\sqrt{2mE}}\] |
| For Photon\[E=pc\] |
| \[\Rightarrow \] \[{{\lambda }_{Ph}}=\frac{hc}{E}\] |
| \[\Rightarrow \] \[\frac{{{\lambda }_{e}}}{{{\lambda }_{Ph}}}=\frac{h}{\sqrt{2mE}}\times \frac{E}{hc}={{\left( \frac{E}{2m} \right)}^{1/2}}\frac{1}{c}\] |
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