Respuesta :
Answer:
a) atoms/cell = 8 atoms
b) FE = 0.3876
Explanation:
You have the following data:
ao=0.45258 nm
bo=0.45186 nm
co=0.76570 nm
density=p=5.904 g/cm^3
atomic weight=69.72 g/mol
Avogadro number = 6.02x10^23 atom/mol
a) The number of atoms per cell is calculated by clearing it from the density formula:
atoms/cell = (px(cell volume)x(Avogadro number))/atomic weight
cell volume = aoxboxco = (0.45258x10^-7cm)x(0.45186x10^-7cm)x(0.76570x10^-7cm) = 1.5659x10^-22 cm^3
replacing values:
atoms/cell = ((5.904 g/cm^3)x(1.5659x10^-22 cm^3)(6.02x10^23 atoms/cell))/69.72 g/mol = 7.9 atoms = 8 atoms
b)the packing factor is calculated by:
FE = ((atoms/cell)x(atom volume))/cell volume
atom volume = 4pixr^3/3 = 4pix(0.1219x10^-7 cm)^3/3 = 7.5875x10^-24 cm^3
FE = (8x7.5875x10^-24)/(1.5659^-22 cm^3) = 0.3876
The number of atoms in each unit cell and the packing factor in the unit cell are;
a) Number of atoms in each unit cell = 8 atoms
b) Atomic packing factor = 0.3876
We are given;
a_o = 0.45258 nm ≈ 0.45258 × 10⁻⁷ cm
b_o = 0.45186 nm = 0.45186 × 10⁻⁷ cm
c_o = 0.76570 nm = 0.7657 × 10⁻⁷ cm
Atomic radius; r = 0.1218 nm = 0.1218 × 10⁻⁷
density; ρ = 5.904 g/cm³
Atomic weight = 69.72 g/mol
Avogadro's number = 6.02 × 10²³ atom/mol
a) The number of atoms per cell is calculated by clearing it from the equation;
Number of atoms per cell = (ρ × cell volume × Avogadro number)/atomic weight
Where;
cell volume = a_o × b_o × c_o
Cell volume = 0.45258 × 10⁻⁷ × 0.45186 × 10⁻⁷ × 0.7657 × 10⁻⁷
Cell volume = 1.5659 × 10¯²² cm³
Thus;
Number of atoms per cell = (5.904 × 1.5659 × 10¯²² × 6.02 × 10²³)/69.72
Number of atoms per cell = 7.9 atoms
Number of atoms per cell ≈ 8 atoms
B) Formula for the packing factor is calculated from the formula:
Packing Factor = (number of atoms per cell x atom volume)/cell volume
Formula for atom volume is;
Atom volume = 4πr³/3
Atom volume = (4π × 0.1218 × 10⁻⁷)³/3
Atom volume = 7.5875 × 10¯²⁴ cm³
Thus;
Packing Factor = (8 x 7.5875 x 10¯²⁴)/(1.5659¯²²)
Packing Factor = 0.3876
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