Answer
Shortest: $4.35\times10^{-2}nm$
Longest: ~ 1 nm
Work Step by Step
The smallest wavelength X-ray has the most energy. The incoming electrons have an energy of 28.5 keV, so that is the maximum energy of an x-ray photon.
In this problem, the value of hc is useful. Use the result stated in Chapter 27, Problem 29, $hc=1240\;eV \cdot nm$.
Use equation 27–4, E = hf, and recall that $\lambda f = c$.
$$\lambda = \frac{c}{f}=\frac{hc}{hf}=\frac{1240\;eV \cdot nm }{28500eV}=4.35\times10^{-2}nm$$
The longest wavelength (lowest energy) photon is at the boundary of what is considered to be the x-ray region, approximately 1 nm.