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Concept explainers
Interpretation:
Given the atomic radius of solid Argon, its density has to be calculated.
Concept Introduction:
In a crystalline solid, the components are neatly stacked and closely packed in a regular pattern. The components are imagined as spheres. The two major types of close packing of the spheres in the crystal are – hexagonal close packing and cubic close packing. Cubic close packing structure has face-centered cubic (FCC) unit cell.
In face-centered cubic unit cell, each of the six corners is occupied by every single atom. Each face of the cube is occupied by one atom.
Each atom in the corner is shared by eight unit cells and each atom in the face is shared by two unit cells. Thus the number of atoms per unit cell in FCC unit cell is,
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Answer to Problem 12.114QP
The density of solid Argon is
Explanation of Solution
Solid Argon has cubic close packing structure with face-centered cubic unit cells. The atomic radius of solid Argon is given. The formula for the edge length of the cubic unit cell is known as
Accordingly calculate volume of FCC unit cell as shown below –
Each unit cell contains 4 Ar atoms. Therefore four times the average mass of one Argon atom gives mass of a unit cell of solid Argon. Hence the mass of a unit cell of solid Argon.
Mass and volume of the unit cell is calculated in the previous steps. By substituting the values in the formula,
The density of solid Argon is,
The density of solid Argon was determined using the relation between edge length of the FCC unit cell and atomic radius.
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Chapter 12 Solutions
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