The zincblende structure of ZnS has the relatively large sulfide ions arranged at the lattice points of a face-centered cubic structure.The edge length of this cubic unit cell is 540.9 pm.Determine the density of zincblende. A)0.244 g/cm³ B)1.02 g/cm³ C)2.05 g/cm³ D)4.09 g/cm³ E)8.18 g/cm3

Question

Quizplus · Accepted Answer

First, we need to calculate the mass of one unit cell of ZnS.

The edge length of the cubic unit cell is given as 540.9 pm or 5.409 Å. Since the lattice points are occupied by sulfur ions, the radius of the sulfide ion can be calculated using the edge length:

r = (a/2) = (5.409 Å/2) = 2.705 Å

The volume of each sulfide ion is (4/3)πr³, and since there are four sulfide ions per unit cell, the total volume of the sulfide ions in one unit cell is:

Volume of sulfide ions = 4 × (4/3)πr³ = 4 × (4/3)π(2.705 Å)³ = 104.43 Å³

Similarly, the volume of each zinc ion is zero (assuming it is a point particle), so the total volume of the unit cell is also 104.43 Å³.

The atomic mass of Zn is 65.38 g/mol, and the atomic mass of S is 32.06 g/mol. The mass of one unit cell is therefore:

Mass of unit cell = (4 × atomic mass of S) + (4 × atomic mass of Zn) 
                            = (4 × 32.06 g/mol) + (4 × 65.38 g/mol) 
                            = 388.08 g/mol

Finally, we can calculate the density using the mass and volume:

Density = mass/volume = 388.08 g/mol / 104.43 Å³ 
               = (388.08 g/mol / 1.661 × 10⁻²⁴ g) / (104.43 Å³ / (1 × 10⁻²⁸ m³)) 
               = 5.76 × 10³ kg/m³ or 4.09 g/cm³

Therefore, the best choice is D, 4.09 g/cm³.

The Zincblende Structure of ZnS Has the Relatively Large Sulfide