A student sets up Young's double slit experiment with electrons of momentum p incident normally on the slits of width $w$ separated by distance $d.$ In order to observe interference fringes on a screen at a distance $D$ from the slits, which of the following conditions should be satisfied?

$($a$)\frac{}{p}>\frac{Dw}{d}$

$($b$),\frac{}{p}>\frac{dw}{D}$

$($c$)\frac{}{p}>\frac{d^2}{D}$

$($d$),\frac{}{p}>\frac{d^2}{\sqrt[\phantom{2}]{Dw}}$