Answer :
Answer:
a) [tex]N_{particle}[/tex] = 4.02 = 4 atoms / unit cell
b) Density = 7.31 g/(cm)³
Explanation:
a)
Tetragonal structure, one of the structural groups to which crystalline solids may be classified. In this process, the crystals are referred to as three mutually perpendicular poles, i.e 90° from each other, two of which are of equal length. It has a square base with area a×a and height c.
Given data:
a = 0.459 nm
c = 0.495 nm
Atomic packing factor is the measurement of the actual volume of the imaginary atomic scale "shell" filled by the atoms. In simple words, it is the ratio of volume of atoms within the unit cell to the total volume of the unit cell.
atomic packing factor = ( volume of atoms within the unit cell) / (total volume of the unit cell)
APF = [tex]\frac{N_{particle}. V_{particle}}{V_{unitcell} }[/tex]
where [tex]N_{particle}[/tex] is the number of particles in the unit cell,[tex]V_{particle}[/tex] is the volume of each particle, and [tex]{V_{unitcell}[/tex] is the volume occupied by the unit cell.
Given data:
APF = 0.693
Atomic radius = r = 0.1625 nm
Volume of unit cell = a × a × c
= 0.459 × 0.459 × 0.495
= 0.1043 (nm)³ = 1.043 × 10⁻²⁸ m³
Volume of each particle = 4/3(π)r³
4/3(3.14)(0.1625)³ = 0.0179 (nm)³ = 1.79 × 10⁻²⁹ m
APF = [tex]\frac{N_{particle}. V_{particle}}{V_{unitcell} }[/tex]
0.693 = [[tex]N_{particle}[/tex] × 0.0179 (nm)³] ÷ 0.1043 (nm)³
[tex]N_{particle}[/tex] = 4.02 = 4 atoms / unit cell
b)
Density is the mass of an object per unit volume. It tell us that how much mass of an object in one unit volume.Metals has higher density than gases because atoms of metals are closely packed than gases. General formula for density (d) is
d = mass/Volume
To calculate density here, we use density formula related to molecules.
No. of atoms = (Avogadro's number×density×Volume)/(Molecular weight)
The atomic weight of indium = 114.82 g/mol
Avogadro's number = 6.022 × 10²³
Theoretical density = D = ?
density = (4 × 114.82 ) / (6.022 × 10²³ × 1.043 × 10⁻²⁸)
Density = 7.31 g/(cm)³