For high-energy electron diffraction in a TEM, another estimate of the precision of diffraction angles can be provided by the uncertainty principle: px We do not know the specific plane that scatters the electron, so x is set by the number of scattering lattice planes, N, times the interplanar spacing, d: so that x=Nd. (a) Given the de Broglie equation and the uncertainty principle, how do small changes in the wavelengths of electrons scale with N? (b) Use your answer to (a) to show how small errors in the diffracting angle scales with N