Answer:
de-Broglie put forward the bold hypothesis that moving particles of matter should display wave- like properties under suitable conditions. He reasoned that nature was symmetrical and that the two basic physical entities, matter and energy, must have symmetrical character. If radiation shows a dual nature, so should matter. For a particle of mass m, \[K=\frac{{{p}^{2}}}{2m}\] and \[p=\frac{h}{\lambda }\] \[\therefore \] \[K=\frac{{{h}^{2}}}{2m{{\lambda }^{2}}}\] Also, \[{{E}_{photon}}=\frac{hc}{\lambda }\] \[\therefore \] \[\frac{K}{{{E}_{photon}}}=\frac{h}{2mc\lambda }\] or \[{{E}_{photon}}=\left( \frac{2\lambda mc}{h} \right)K.\]
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