Answer
$3.9\times10^{-3}nm$; No.
Work Step by Step
In this problem, the value of hc is useful. Use the result stated in Problem 29, $hc=1240\;eV \cdot nm$.
Use equation 27–4, E = hf, and recall that $\lambda f = c$.
$$\lambda = \frac{c}{f}=\frac{hc}{hf}=\frac{1240\;eV \cdot nm }{320000eV}=3.9\times10^{-3}nm$$
Diffraction effects are significant when the opening is about the same size as the wavelength. We do not expect significant diffraction here.