Electron microscopes can obtain images with several hundredfold higher resolution than optical microscopes because of the short wavelength obtainable from a beam of electrons. For electrons moving at speeds close to c, the speed of light, the expression for the de Broglie wavelength needs to be corrected for relativistic effects:
λ = h { 2meV [1 + eV/(2mc2 )] }–1/2
where h is Planck’s constant, m is the mass, e is the charge on the electron, and V is the potential difference through which the electrons are accelerated.
(a) Use the expression above to calculate the de Broglie wavelength of electrons accelerated through 50 kV.
(b) Is the relativistic correction important at this energy (a typical energy for an electron microscope)?