Answer
The electron must be accelerated through a potential difference of at least $~~12.4~kV$
Work Step by Step
We can find the energy associated with a wavelength $\lambda = 0.100~nm$:
$E = \frac{hc}{\lambda}$
$E = \frac{(6.626\times 10^{-34}~J\cdot s)(3.0\times 10^8~m/s)}{0.100\times 10^{-9}~m}$
$E = 1.9878 \times 10^{-15}~J$
$E = (1.9878 \times 10^{-15}~J)(\frac{1~eV}{1.6\times 10^{-19}~J})$
$E = 1.24\times 10^4~eV$
$E = 12.4~keV$
The electron must be accelerated through a potential difference of at least $~~12.4~kV$
