In an electron microscope, the electrons are accelerated under a potential difference, V; the potential energy equals the kinetic energy of the accelerated electrons:
......................................................... (17.2)
......................................................... (17.3)
where, e, m0, and v are the charge, the rest mass, and the velocity of the electrons, respectively.
Substituting for v in equation 17.1:
......................................................... (17.4)
Equation 17.4 shows that the wavelength of the electrons depends on the accelerating potential, V. At very large accelerating potentials, the electron velocity can approach the velocity of light, c; the relativistic effects become significant at accelerating potentials higher than ~100 kV. Incorporating the relativistic effects in the expression for wavelength given in equation 17.4 gives:
......................................................... (17.5)
Substituting the values of h, e, m0, and c in equation 17.5 gives:
nm ......................................................... (17.6)