Answer
$24.9\;pm$
Work Step by Step
The shortest wavelength in the spectrum is the cutoff wavelength , which is emitted when an incident electron loses its full kinetic energy $K_0$ in a single collision:
$\lambda_{min}=\frac{hc}{K_0}$ .............................$(1)$
Given: $K_0=50\;keV=50\times10^3\times1.6\times10^{-19}\;J=8\times10^{-15}\;J$
Substituting, the given values of $K_0$ in Eq. $1$, we obtain
$\lambda_{min}=\frac{6.63\times 10^{-34}\times3\times 10^{8}}{8\times 10^{-15}}\;m$
or, $\lambda_{min}\approx 2.49\times 10^{-11}\;m$
or, $\lambda_{min}=24.9\;pm$
