Answers_to_assn_1 - CHEM 123 Assignment 1 page 1 of 10 1...

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CHEM 123: Assignment # 1 page 1 of 10 1. Simple cubic packing. The crystal lattic and unit cell for simple cubic packing are shown below. a) # spheres = ( ) ( 1 8 sphere/corner 8 corners ) = 1 sphere The coordination number of each sphere is 6. To see this, focus on an “interior” sphere such as sphere “A” in the figure on the left. That sphere is in contact with 6 other spheres – the one above it, the one below, the one in front, the one behind, the one to its left and the one to its right. b ) If the radius of each sphere is “ R ” then the edge length of the unit cell is a = 2 R c) The volume of the unit cell is V cell = a 3 = 8 R 3 There is one full sphere contained within the unit cell so the volume of spheres contained within the unit cell is 3 spheres 4 3 V R = π . 3 4 3 3 0.5236 6 8 spheres cell V R Packing Efficiency V R π π = = = = 2. Show that the following data are consistent with the fact that silver metal crystallizes in a face-centred cubic lattice: Edge length of unit cell, a = 408 pm Density of silver, 10.6 g cm 3 Atomic weight of silver, 107.9 g mol 1 , Avogadro's number, N A = 6.022 × 10 23 If silver crystallizes in a face-centred cubic lattice, then 1 23 1 3 10 3 107.9 g mol 6.022 10 atoms mol (4 atoms) 10.6 g cm (408 10 cm) cell cell m V d × × = = = A The calculated density agrees well with the observed density.
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