Consider a hypothetical element whose structure can be based on either of the following: a)cell a – a base-centered tetragonal containing two atoms per cell, at 0 0 0 and ½ ½ 0, for which a = 2å and c = 3å b)cell b – simple tetragonal with one atom per cell at 0 0 0 (hint: are "a" and "c" the same for a and b? ) this is shown in c& s, fig. 2-11. determine simplified structure factor equations for each cell and the position (2 values) of the first four lines that would be observed (|f2|  0)on a powder pattern made with cu k radiation. plot the 2 values of these lines in the manner of fig 10-2 (c& s) and label each line with its indices relative to cell a and cell b. draw the two cells in the proper relation to one another, and show that the indices of any one observed line (other than the obvious 0 0 l) refer to the same plane of atoms. this problem illustrates several points: (1) we can choose any cell we wish (even a cell that is not one of the recognized bravais lattices); (2) the miller indices of any given plan depend on the choice of the cell; (3) the diffraction pattern of a material is independent of the choice of cell