Answer:
The magnitude of the wavelength of de-Broglie waves associated with a moving football is extremely small \[\left( \lambda =\frac{h}{mv}<{{10}^{-34}}m \right),\] which is much less than that of visible region and therefore they are not visible. Wavelength of photon \[=\lambda \] \[\therefore \] Energy of photon, \[{{E}_{p}}=hc/\lambda \] ?(i) Kinetic energy of electron, \[{{E}_{e}}=\frac{1}{2}m{{v}^{2}}\] or \[m{{v}^{2}}=2{{E}_{e}}\] or \[v=\sqrt{\frac{2{{E}_{e}}}{m}}\] \[(\because {{m}_{e}}=m)\] de-Broglie wavelength of electron \[\lambda =\frac{h}{mv}\] \[=\frac{h}{\sqrt{2{{E}_{e}}m}}\] or \[{{E}_{e}}=\frac{{{h}^{2}}}{2{{\lambda }^{2}}m}\] ?(ii) On dividing Eq. (i) by Eq. (ii), we get \[\frac{{{E}_{p}}}{{{E}_{e}}}=\frac{hc}{\lambda }\cdot \frac{2{{\lambda }^{2}}m}{{{h}^{2}}}=\frac{2\lambda mc}{h}\] or \[{{E}_{p}}=\frac{2\lambda mc}{h}\cdot {{E}_{e}}\]
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