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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,
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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
- Calculate the unit cell edge length of copper metal, which has an fcc arrangement. The radius of a copper atom is 126 pm.arrow_forward8.98 If you know the density of material and the length of the edge of its cubic Iattice, how would you determine if it is face-centered cubic, body-centered cubic, or simple cubic Would you have to look up any information?arrow_forwardThe coordination number of uniformly sized spheres in a cubic closest-packing (FCC) array is 12. Give the coordination number of each atom in (a) a simple cubic lattice. (b) a body-centered cubic lattice.arrow_forward
- The density of polonium metal is 9.2 g/cm3. If the extended lattice of polonium exhibits a simple cubic unit cell, estimate the atomic radius of polonium.arrow_forward• describe the arrangement of atoms in the common cubic crystal lattices and calculate the packing efficiency for a lattice.arrow_forwardVanadium metal has a density of 6.11 g/cm3. Assuming the vanadium atomic radius is 132 pm, is the vanadium unit cell primitive cubic, body-centered cubic, or face-centered cubic?arrow_forward
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- A certain element exists in a face-centered cubic structure. The atomic radius of an atom of this element is 125 pm. Calculate the density of this element in g/cm3. (Assume the element has a molar mass of 61.5 g/mol.)arrow_forwardNickel has a face-centered cubic structure and has a density of 8.90 g/cm3. Calculate its atomic radius?arrow_forward8. An element with atomic mass 106.3amu crystallizes in a face–centered cubic unit cell. Its density is 12.9 g/cm3 at 27°C. Calculate the atomic radius of an atom of the element in centimeters.arrow_forward
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