Answer
$x=0.45\mu m$
Work Step by Step
$\lambda=\frac{h}{p}$
$KE=\frac{m_nv^2}{2}=\frac{p^2}{2m_n}$
$p=\sqrt{2m_nKE}$
$\lambda=\frac{h}{\sqrt{2m_nKE}}$
$d\frac{x}{l}=m\lambda$
$x=\frac{l\lambda}{d}=\frac{lh}{d\sqrt{2m_nKE}}=0.45\mu m$
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