Concept explainers
Interpretation:
The density of nickel having face-centered cubic unit cell is given and its atomic radius has to be determined.
Concept introduction:
In packing of atoms in a crystal structure, the atoms are imagined as spheres and closely packed in a regular pattern. 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 52E
Answer
The radius of nickel atom is
Explanation of Solution
Explanation
Calculate the mass of a unit cell.
Each unit cell contains 4 Ni atoms. Therefore four times the average mass of one Ni atom gives mass of a unit cell.
Calculate the volume and edge length of the unit cell.
The volume ‘a3’ of the unit cell is calculated using
Calculate the radius of Ni atom.
The side length of fcc unit cell is given as
Conclusion
The radius of the nickel atom is determined using the concept of side length of the FCC unit cell and its relation with density given.
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Chapter 9 Solutions
Chemistry: An Atoms First Approach
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