The accompanying figure shows three different crystallographic planes for a unit

Question

The accompanying figure shows three different crystallographic planes for a unit cell of some hypothetical metal. The circles represent atoms. (a) To what crystal system does the unit cell belong? (b) What would this crystal structure be called? (c) If the density of this metal is 18.91 g/cm3, determine its atomic weight. To what crystal system does the unit cell belong? (b) What would this crystal structure be called? (c) If the density of this metal is 18.91 g/cm3, determine its atomic weight.

Explanation / Answer

(a) This unit cell belongs to the orthorhombic crystal system since a = 0.25 nm, b = 0.30 nm, c = 0.20 nm, and = = = 90°.

(b) This crystal structure would be called face-centered orthorhombic since the unit cell has orthorhombic symmetry, and an atom is located at each of the corners, as well as at each of the face centers.

(c) In order to compute its atomic weight, with n = 4; thus

A = rho*Vc*NA/n = (18.91)(2.0)(2.5)(3.0) (10-24)(6.02*1023)/4 = 42.7 g/mol

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