Draw the reciprocal lattice and the ewald sphere where the lattice is a=4Å and its wavelength λ=1.542Å is diffracted on plane (200).

At room temperature, the diffractogram of a cubic material with lattice parameter of 10Å presents a peak at 2θ = 20o. At a higher temperature, the lattice parameter has expanded 20%. Calculate the 2q value of the diffraction peak of the material at the high temperature. λλ is fixed. Do not assume a particular (hkl) set of values, nor a value for λ.

Consider scattering with electrons of 54 eV on a crystal with planes separated by 0.22 nm. How many diffraction peaks should be expected? Justify your answer

A highly collimated (parallel) beam of electrons is shot through a single slit of width 17.5μm. The electrons are moving with a speed of 7.357.35km/s. When they hit the screen, located at distance 1.57m away, the distribution of hitting positions makes a pattern with a central peak and minima on either side. What is the width of the central peak (equivalently, distance between the minima on either side)?   The mass of an electron is 9.11×10​^−31​​ kg.