= Solution
For an aligned narrower slit placed immediately after the first, uniform illumination gives <Transmission coefficient>[transmission probability] $\boxed{d/w}$. Conditional on passage the same normalized formula applies with $w$ replaced by $d$ and central-lobe <momentum> scale $h/d$. Position rms is $d/\sqrt{12}$, while the exact hard-edge rms $\Delta p_x$ is infinite. Thus the source's finite “uncertainty” can only mean a characteristic diffraction width; the rigorous Heisenberg inequality is not violated, and smoothing the edges restores finite rms moments satisfying it.
A 10 keV X-ray has $\lambda\simeq0.124$ nm. The ideal position-filter <probability> and <momentum> formula at fixed aperture widths are unchanged, since the <Fourier transform> involves $h$ and the aperture geometry. Its larger total <momentum> makes the angular diffraction width smaller, approximately $\lambda/d$. Real slit-material transmission and absorption are additional experimental issues.
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