Question

What experimental evidence supports de Broglie's idea that electrons have wave like properties?

Answer 1

Electrons shot at a double slit produces an interference pattern on a screen placed behind the double slits, much like waves would do.
This verifies that electron particles also have a wave nature and have a de Broglie wavelength given by `lambda=h/p`.

However when the electrons are observed and measured as they pass the double slit, the interference pattern vanishes and is replaced with 2 bands on the screen, indicating a particle nature.

The conclusion is thus that all waves have particle properties and all particles have wave properties, and which property becomes more dominant depends on the situation and observation being made.