Answer
23.0 pm.
Work Step by Step
The KE is much less than the rest energy of an electron. We may use nonrelativistic relationships. Calculate the wavelength using equation 27–8.
$$KE=\frac{p^2}{2m}$$
$$p=\sqrt{2m(KE)}$$
$$\lambda=\frac{h}{p}=\frac{h}{\sqrt{2m(KE)}}$$
$$\lambda=\frac{6.626\times10^{-34}J \cdot s }{\sqrt{2(9.11\times10^{-31}kg)(2850eV)(1.60\times10^{-19}J/eV)}}$$
$$=2.30\times10^{-11}m= 23.0\times10^{-12}m $$
As discussed in sections 25-7 and 25-8, the microscope's resolution is about the size of the wavelength of the electron/radiation used to view an object.