Answer
3.5 pm.
Work Step by Step
The theoretical limit of resolution is the wavelength of the electron. We find the wavelength from the momentum. To calculate the momentum, relate it to the kinetic energy and rest energy using the result cited on page 768 (Problem 26-45).
$$\lambda=\frac{h}{p}=\frac{hc}{\sqrt{KE^2+2mc^2KE}}$$
The kinetic energy of the electron is 110 keV.
$$\lambda=\frac{(6.626\times10^{-34}J\cdot s)(3.00\times10^8 m/s)}{(1.60\times10^{-19}J/eV)\sqrt{(110\times10^3 eV)^2+2(0.511\times10^6 eV) (110\times10^3 eV)}}$$
$$\lambda=3.5\times10^{-12} m$$
This is the theoretical limit of resolution for the electron microscope.
