What reasoning let deBroglie to put forward the concept of matter waves? Show that the energy og photon is  times the kinetic energy of particle.

The concept of matter waves was put forward by de Broglie in his PhD thesis in 1924.

He proposed that just as light has both wave-like and particle-like properties, electrons (matter) also have wave-like properties. 

He thought that just as wave and corpuscular properties exist for photons, it should exist for matter too.

This led him to propose the theory of matter waves.