question_answer

What reasoning led de-Broglie to put forward the concept of matter waves? The wavelength, \[\lambda \], of a photon, and the de-Broglie wavelength associated with a particle of mass 'm', has the same value, say \[\lambda \]. Show that the energy of photon is \[\frac{2\lambda mc}{h}\] times the kinetic energy of the particle.  

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             \[{{E}_{photon}}=\left( \frac{2\lambda mc}{h} \right)K.\]