e45_hw_2 - E45 HW02 Due September 10, 2010 Reference: J.F....

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E45 HW02 Due September 10, 2010 Reference: J.F. Shackelford, Introduction to Materials Science for Engineers, 6 th Edition, Prentice Hall, New Jersey (2005) Problem 1 2.5 An Al 2 O 3 whisker is a small single crystal used to reinforce metal-matrix composites. Given a cylindrical shape, calculate the number of Al atoms and the number of O atoms in a whisker with a diameter of 1 μm and a length of 30 μm. (The density of Al 2 O 3 is 3.97 Mg/m 3 .) SOLUTION V x density→ mass (/molar mass)→ number of moles (Avogadro's number)→ number of atoms Volume of cylinder= π r 2 h = π (0.5 μm) 2 (30 μm) = 47.13 μm 3 = 4.713*10- 5 m 3 Mass of Al 2 O 3 = (Volume of cylinder) (density of Al 2 O 3 ) = (4.713*10- 5 m 3 ) (3.97 Mg/m 3 ) = 1.871*10 -4 Mg = 187.1 g Moles of Al 2 O 3 = (Mass of Al 2 O 3 ) / (Molar Mass Al 2 O 3 ) = (187.1 g) / (102 g/mol)= 1.834 mol Al 2 O 3 Number of Al atoms= (Moles Al 2 O 3 ) (2 mol Al/mol Al 2 O 3 ) (Avogadro's number) = (1.834 mol Al 2 O 3 ) (2) (6.022*10 23 atoms Al/mol) = 2.21*10
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e45_hw_2 - E45 HW02 Due September 10, 2010 Reference: J.F....

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