Einstein continued to extend his theories around the interaction of photons and atomic particles, going so far as to hypothesize that photons could have momentum, also a particle property, even though they had no mass.
In 1922, American physicist Arthur Compton shot an X-ray photon at a graphite target to observe the collision between the photon and one of the graphite atom’s electrons. Compton observed that when the photon collided with an electron, a photoelectron was emitted, but the original X-ray was also scattered and emitted, but with a longer wavelength (indicating it had lost energy).
Further, the longer wavelength also indicated that the photon must have lost momentum. A detailed analysis showed that the energy and momentum lost by the X-ray was exactly equal to the energy and momentum gained by the photoelectron. Compton therefore concluded that not only do photons have momentum, they also obey the laws of conservation of energy and conservation of momentum!
In 1923, French physicist Louis De Broglie took Compton’s finding one step further. He stated that if EM waves can behave as moving particles, it would only make sense that a moving particle should exhibit wave properties. De Broglie’s hypothesis was confirmed by shooting electrons through a double slit, similar to Young’s Double Slit Experiment, and observing a diffraction pattern. The wavelength of a moving particle, now known as the De Broglie Wavelength, is given by: 
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