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A pure metal crystallizes in a face-centered cubic (FCC) lattice. The atomic radius of the metal is 100 2 pm and its density is 10.0 g cm ⁻³ . The molar mass of the metal is _________ g mol ⁻¹ . (Nearest integer) (Given : N_A = 6.0 10²³ mol ⁻¹ )

Correct answer

96

Step-by-step solution

For a face-centered cubic (FCC) lattice, the relationship between the edge length a and the atomic radius r is given by: a = 2 2 r Substitute the given atomic radius: a = 2 2 100 2 pm = 400 pm = 4 10⁻⁸ cm The volume of the unit cell is: a^3 = (4 10⁻⁸ cm )^3 = 64 10⁻²⁴ cm ^3 The formula for the density of a unit cell is: d = Z M N_A a^3 For an FCC lattice, the effective number of atoms per unit cell is Z = 4 . Substituting the known values: 10.0 = 4 M 6.0 10²³ 64 10⁻²⁴ 10.0 = 4 M 38.4 M = 384 4 = 96 g mol ⁻¹ Answer:

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