French physicist de Broglie in 1924 proposed that like radiations, matter should also possess both particle and wave like nature. The wavelength of matter waves was given by the formula

(1) According to Einstein mass-energy relation ship , $\mathrm{E}={\mathrm{mC}}^2$  (which supports particle nature)

(2) According to Plank's quantum theory , $\mathrm{E}=\mathrm{h\nu }$ (which supports wave nature)

According to De-Broglie ,

 $$\begin{gathered} {\mathrm{mC}}^2=\mathrm{h\nu } \\ {\mathrm{mC}}^2=\frac{\mathrm{hC}}{\mathrm{\lambda }} \\ \mathrm{\lambda }=\frac{\mathrm{h}}{\mathrm{mC}}\Rightarrow \mathrm{\lambda }=\frac{\mathrm{h}}{\mathrm{mv}} (\because \mathrm{velocity} \mathrm{of} \mathrm{particle} \mathrm{was} \mathrm{considered}) \end{gathered}$$