Answer:
Zinc blende
Step-by-step explanation:
Step 1. Calculate the volume of the unit cell
V = l³
V = (0.57)³
V = 0.1852 nm³ Convert to m³
V = 0.1852 × (10⁻⁹)³
V = 1.852 × 10⁻²⁸ m³ Convert to cm³
V = 1.852 × 10⁻²⁸ × 100³
V = 1.852 × 10⁻²⁸× 10⁶
V = 1.852 × 10⁻²² cm³
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Step 2. Calculate the mass of a unit cell
ρ = m/V Multiply each side by V
m = Vρ
m = 1.852 × 10⁻²² × 2.10
m = 3.889 × 10⁻²² g Convert to u
m = 3.889 × 10⁻²² × 1/(1.661 × 10⁻²⁴)
m = 234 u
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Step 3. Calculate the number of formula units per unit cell
AX = 28.5 + 30.0
AX = 58.5u
Formula units = 234/58.5= 4.00 ≈ 4
There are 4 formula units per unit cell
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Step 4. Determine the type of unit cell
NaCl = simple cubic cell = 1 formula unit
CsCl = one-formula-unit cell = 1 formula unit
The zinc blende structure is shown below. The A atoms are FCC, while the X atoms are at half the tetrahedral sites.
A atoms = 8×⅛ + 6×½ = 1 + 3 = 4
X atoms = 4×1 = 4
The zinc blende structure has four formula units.
