Name _____________________________ Group members: X-ray diffraction and Avogadro’s numberAn ultra-pure sample of silicon was found to have the following isotopic composition: 28Si 29Si30SiAtomic % 92.228948 4.669981 3.101071Nuclide Mass (amu) 27.9769286 28.9764969 29.9737722Precise density measurements show this silicon sample to have a density of 2.3290017 g/cm3 andhigh-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’snumber, NA, using the type of dimensional analysis that you learned in General Chemistry. (Theoriginal paper is Physical Review Letters (1974) 33, 463, and it provided a 30-fold increase in theaccuracy to which NA could be calculated.) Based on the measured density, cubic latticeconstant, and your knowledge of the contents of the crystal structure of Si, you will calculate twoimportant intermediate quantities before calculating an ultra-accurate value of NA. GIVE ALL ANSWERS TO THE MAXIMUM NUMBER OF SIGNIFICANT FIGURESTHAT CAN BE ACCURATELY REPORTED, using the rules that you were taught inGeneral Chemistry. Make sure that you do not inappropriately truncate any values prior toreporting 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 cellNA = Avagadro’s # (1/mol)V = cell volumeVNnMAName _____________________________ Group members: (1)(2)Name _____________________________ Group members:
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