The atomic radius of metal X is 125 picometers (pm) and a crystal of metal X has a unit cell that is face-centered cubic. Calculate the density of metal X (atomic weight = 42.3 g/mol).

Question

Patrick Moyer

Chemistry

22 April, 07:36

The atomic radius of metal X is 125 picometers (pm) and a crystal of metal X has a unit cell that is face-centered cubic. Calculate the density of metal X (atomic weight = 42.3 g/mol).

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Ramiro Shelton · Answer 1

I guess you mean 1.40 x 10^2 pm. An FCC cell contains 4 atoms, and the face diagonal embraces two atomic diameters. So the face diagonal of the Metal X cell is 560 pm, and the edge of this cell is 560 pm/sqrt (2) = 396 pm. The volume of the cell is 6.21 x 10^ (-29) m^3, and the mass of the cell is 4*42.3 g / (6.022E23) = 2.81 x 10^ (-22) grams or 2.81 x 10^ (-25) kg. The density of metal X is:

2.81E (-25) kg/6.21E (-29) m^3 = 4525 kg/m^3 or 4.525 g/cm^3.