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  • The radius of an atom is . If the crystal lattice is face-centred cubic, what is the packing efficiency of the

The radius of an atom is 0.154 nm. If the crystal lattice is face-centred cubic, what is the packing efficiency of the lattice? (Assume that atoms are perfect spheres)

Option: 1

52.4%


Option: 2

68%


Option: 3

74%


Option: 4

90%


Answers (1)

best_answer

For a face-centred cubic lattice, the packing efficiency is given by the expression: (4\pi/3) \times n \times (r)^3 \times 100% / V,where n is the number of atoms per unit cell, r is the radius of the atom, and V is the volume of the unit cell. Substituting the given values, we get:\frac{(4\pi/3) \times 4 \times (0.154 nm)^3 }{ (a^3)}\times 100% where a is the edge length of the unit cell. Simplifying this expression gives us a packing efficiency of approximately 74%.

 

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