Explain how and why the diffraction pattern of electrons passing through a slit depends on their momentum.

To understand this question, we have to consider the wave-particle duality of electrons. When passing through a slit, electrons exhibit a wavelike property- they diffract or spread out like a wave passing through a narrow gap. The De Broglie wavelength tells us about the wave-particle relationship:

λ = h/mv

where λ is the wavelength, h is planks constant, m is the mass and v is velocity. As momentum p = mv, a smaller momentum will result in a longer wavelength. The diffraction or spread of a wave passing through a slit depends on the wavelength- the longer the wavelength, the more the light spreads out. Finally, we can consider (through a diagram) that more spread out waves will have a more dispersed diffraction pattern. Therefore, electrons with smaller momentum will produce a more diffuse diffraction pattern.