Concept explainers
Calcium metal crystallizes in a face-centered cubic unit cell with a cell edge length of 558.84 pm. Calculate (a) the radius of a calcium atom in angstroms (A) and (b) the density of calcium metal in g/crn3.
Interpretation:
Edge length of unit cell of Calcium is given. Its density and atomic radius have to be determined.
Concept Introduction:
In crystalline solids, the components are packed in regular pattern and neatly stacked. The components are imagined as spheres and closely packed. This phenomenon is called “close packing” in crystals. 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,
Answer to Problem 12.120QP
Atomic radius of Calcium is
Density of Calcium is
Explanation of Solution
The edge length of the unit cell of Calcium is related to the atomic radius of the Calcium as
The atomic radius of the Calcium is calculated in the previous step. The formula for the edge length of the cubic unit cell is known as
Each unit cell contains 4 Ca atoms. Therefore four times the average mass of one calcium atom gives mass of a unit cell.
Mass and volume of the unit cell is calculated in the previous steps. By substituting the values in the formula,
The atomic radius and density of Calcium have been determined.
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Chapter 12 Solutions
Chemistry: Atoms First
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