Equation 4-17 on page 137 of Cullity describes the quantity "M" in the Debye-Waller exponential factor, f = f0 exp(-M), as M = (1/2)(u q)2, where f0 is the atomic scattering factor, q = 4p/l sin(q), and u is the root mean square (RMS) displacement of the atom due to thermal fluctuations. -Show that the expression for M above follows that given by Cullity in equation 4-17. -Show that the intersection of an atomic d-spacing described by a Gaussian distribution function with the scattering vector q (where q is the difference in momentum between the incident beam and the scattered beam) could lead to this expression for "M". (Refer to Cullity page 495 in appendix 1. You will need to look up the meaning of a Gaussian distribution if you do not know it. The standard deviation of the inverse d-spacing is apparently related to "u".)