Concept explainers
(a)
Interpretation: The density of bcc iron when the radius of an iron atom is given to be
Concept introduction: The density of a unit cell is calculated by the formula,
The mass of a unit cell is calculated by the formula,
To determine: The density of bcc iron when the radius of an iron atom is
(a)
Answer to Problem 12.95AP
Solution
The density of bcc iron is
Explanation of Solution
Explanation
The density of bcc iron is calculated by the formula,
The number of atoms in the unit cell is two when iron has the bcc structure.
The
Substitute these values in the formula of mass of the unit cell,
The mass of bcc
Figure 1
From Figure 1, the relationship between the radius of the iron sphere and the edge length of the unit cell is determined by the formula,
Face diagonal is calculated by the formula,
Body diagonal is calculated by the formula,
Thus, from equations (1) and (2),
The volume of the unit cell
Since,
The volume is calculated by the formula,
The volume of the unit cell in centimeters is,
The density of the unit cell is calculated by the formula,
Substitute the values of mass and that of volume of the unit cell,
Therefore, the density of bcc iron is
(b)
To determine: The density of hexagonal iron given a volume of unit cell is
(b)
Answer to Problem 12.95AP
Solution
The density of hcp iron is
Explanation of Solution
Explanation
The density of the hcp iron is calculated by the formula,
The number of atoms in the unit cell is two when iron has the hcp structure.
The atomic mass of
Substitute these values in the formula of mass of the unit cell,
The mass of hcp
The unit cell volume of hcp iron is given as
The density of the unit cell is calculated by the formula,
Substitute the values of mass and that of volume of the unit cell,
Therefore, the density of hcp iron is
(c)
To determine: The density of a crystal that has
(c)
Answer to Problem 12.95AP
Solution
The density of hcp iron is
Explanation of Solution
Explanation
The density of such a crystal is calculated by the formula,
Since,
The number of atoms in the unit cell is two when iron has the hcp structure.
The atomic mass of
Substitute these values in the formula of mass of the unit cell,
Similarly,
If silicon has hcp structure, then the number of atoms in the unit cell is two.
The atomic mass of silicon is
Substitute these values in the formula of mass of the unit cell,
Total mass of the crystal is the summation of
The volume of the crystal is
The density of the unit cell is calculated by the formula,
Substitute the values of mass and that of volume of the unit cell,
Therefore, the density of hcp iron is
Conclusion
The density of bcc iron is
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