Question

Richard Feynman criticized that the reason the electron microscope is so poor is that the f value of the lenses is only 1 part to 1000; you do not have a big enough numerical aperture. can you convince potential donors that even an electron microscope that is operating at a low acceleration voltage of 5kV still has a much better resolution than a high end optical microscope?
hint: the resolution r of a microscope is defined as r=0.61*lambda/NA, with NA bring the numerical aperture. compare the electron microscope with a numerical aperature of 10^-3 with an optical microscope, operating with a 550 nm light source and an NA=1.4 objective.

Answer 1

For an accelerating voltage of 5kV, the work done on the electron to accelerate it will be:

W = eV = 5keV

from work-energy theorem, this will be its final kinetic energy (assuming it starts from rest).

K = 5keV = 5000 eV = 8 x 10^-16 J

for this, its momentum will be: p = [2mK]^1/2 = 3.816 x 10^-23 kgm/s

now use the de-Broglie's relation to find the electron's de-Broglie wavelength.

so, the resolution of the electron microscope will be:

whereas, for the optical microscope, the resolution is:

which is more than ten times the resolution of the electron microscope and thus the electron microscope have a better resolution.