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The standard equation for a wave travelling through a double-slit apparatus is

$w=\dfrac{z\lambda}{d}$,

where $w$ is the fringe spacing at the detector screen on the other side of the slits, $z$ is the distance from the slits to the detector screen, $\lambda$ is the wavelength and $d$ is the distance between the two slits.

Would this apply to the double slit experiment for an electron as well?

This would then imply that the equation can be expressed as follows:

$w=\dfrac{zh}{dp}$,

where $h$ is Planck's constant and $p$ is the particles momentum.

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Yes, it applies to particles. Your expression for the "particle version" is correct.

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