Question

What lead de broglie to propose his hypothesis?

Answer 1

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De Broglie's concept was based in two points
i) Since Energy and mass are interrelated so if energy has dual properties,mass also should have i.e. Elementary particles like electron,proton should also possess wave like properties.

ii) Nature loves symmetry.Through this symmetrical consideration De Broglie proposed the bold hypothesis of Matter waves which earned him Nobel Prize.


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Answer 2

most probably particle and wave like nature of electomagnetic radiations.
Furthermore,planks eq. and einstein's eq. E=hv and E=mc^2 helped him to prove his equation giving a relationship between wavelength and mass and velocity of matter