Download Notes on X-ray Diffraction and Avogadro's Number | CHEM 242 and more Study notes Inorganic Chemistry in PDF only on Docsity! Name _____________________________ Group members: X-ray diffraction and Avogadro’s number An ultra-pure sample of silicon was found to have the following isotopic composition: 28Si 29Si 30Si Atomic % 92.228948 4.669981 3.101071 Nuclide Mass (amu) 27.9769286 28.9764969 29.9737722 Precise density measurements show this silicon sample to have a density of 2.3290017 g/cm3 and high-resolution x-ray measurements give a unit cell dimension of 543.10661 pm. Taken together, these data can be used to calculate an extremely accurate value of Avogadro’s number, NA, using the type of dimensional analysis that you learned in General Chemistry. (The original paper is Physical Review Letters (1974) 33, 463, and it provided a 30-fold increase in the accuracy to which NA could be calculated.) Based on the measured density, cubic lattice constant, and your knowledge of the contents of the crystal structure of Si, you will calculate two important intermediate quantities before calculating an ultra-accurate value of NA. GIVE ALL ANSWERS TO THE MAXIMUM NUMBER OF SIGNIFICANT FIGURES THAT CAN BE ACCURATELY REPORTED, using the rules that you were taught in General Chemistry. Make sure that you do not inappropriately truncate any values prior to reporting your results, and that units are clearly indicated. (1) What is the average mass of a Si atom? (2) Using the unit cell and density of Si and an approximate value of NA of 6.022 x 1023, calculate the number of atoms that reside in a single cubic unit cell of Si. Note that in reality, this number must be an integer. While your result from this calculation should be an integer to the limits of your significant figures, you should round this result to an actual integer when you do the calculations for part (3). (3) Using this information, calculate NA as accurately as possible from the data above. Show all work, and use the proper number of significant figures. M = molar mass (g/mol) n = # formula units per cell N A = Avagadro’s # (1/mol) V = cell volume VN nM A Name _____________________________ Group members: (1) (2)
