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An element exists in two crystallographic
modifications with FCC and BCC structures. The
ratio of the densities of the FCC and BCC
modifications in terms of the volumes of their
unit cells (VFCC and VBCC) is?
modifications with FCC and BCC structures. The
ratio of the densities of the FCC and BCC
modifications in terms of the volumes of their
unit cells (VFCC and VBCC) is?
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An element exists in two crystallographic modifications with FCC and B...
Understanding Density in FCC and BCC Structures
The densities of crystallographic structures can be compared based on their atomic arrangements and unit cell volumes. For FCC (Face-Centered Cubic) and BCC (Body-Centered Cubic) structures, the density is influenced by the number of atoms per unit cell and the volume of the unit cell.
Density Formula
The density (ρ) of a crystal structure can be expressed as:
ρ = (n * M) / (V * N)
Where:
- n = number of atoms per unit cell
- M = molar mass of the element
- V = volume of the unit cell
- N = Avogadro's number
Atoms per Unit Cell
- FCC: Contains 4 atoms per unit cell.
- BCC: Contains 2 atoms per unit cell.
Unit Cell Volumes
- The volume of the unit cells for FCC (VFCC) and BCC (VBCC) must be considered when calculating density.
Density Ratio Calculation
To find the ratio of densities (ρFCC / ρBCC):
- Density of FCC:
- ρFCC = (4 * M) / (VFCC * N)
- Density of BCC:
- ρBCC = (2 * M) / (VBCC * N)
Now, taking the ratio:
ρFCC / ρBCC = [(4 * M) / (VFCC * N)] / [(2 * M) / (VBCC * N)]
This simplifies to:
ρFCC / ρBCC = (4 / 2) * (VBCC / VFCC) = 2 * (VBCC / VFCC)
Conclusion
The ratio of the densities of the FCC and BCC modifications is directly proportional to the volumes of their unit cells. The final relationship illustrates how the structural arrangement and atomic packing influence the overall density of materials in different crystallographic forms.
The densities of crystallographic structures can be compared based on their atomic arrangements and unit cell volumes. For FCC (Face-Centered Cubic) and BCC (Body-Centered Cubic) structures, the density is influenced by the number of atoms per unit cell and the volume of the unit cell.
Density Formula
The density (ρ) of a crystal structure can be expressed as:
ρ = (n * M) / (V * N)
Where:
- n = number of atoms per unit cell
- M = molar mass of the element
- V = volume of the unit cell
- N = Avogadro's number
Atoms per Unit Cell
- FCC: Contains 4 atoms per unit cell.
- BCC: Contains 2 atoms per unit cell.
Unit Cell Volumes
- The volume of the unit cells for FCC (VFCC) and BCC (VBCC) must be considered when calculating density.
Density Ratio Calculation
To find the ratio of densities (ρFCC / ρBCC):
- Density of FCC:
- ρFCC = (4 * M) / (VFCC * N)
- Density of BCC:
- ρBCC = (2 * M) / (VBCC * N)
Now, taking the ratio:
ρFCC / ρBCC = [(4 * M) / (VFCC * N)] / [(2 * M) / (VBCC * N)]
This simplifies to:
ρFCC / ρBCC = (4 / 2) * (VBCC / VFCC) = 2 * (VBCC / VFCC)
Conclusion
The ratio of the densities of the FCC and BCC modifications is directly proportional to the volumes of their unit cells. The final relationship illustrates how the structural arrangement and atomic packing influence the overall density of materials in different crystallographic forms.
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An element exists in two crystallographic modifications with FCC and BCC structures. The ratio of the densities of the FCC and BCC modifications in terms of the volumes of their unit cells (VFCC and VBCC) is?
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An element exists in two crystallographic modifications with FCC and BCC structures. The ratio of the densities of the FCC and BCC modifications in terms of the volumes of their unit cells (VFCC and VBCC) is? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about An element exists in two crystallographic modifications with FCC and BCC structures. The ratio of the densities of the FCC and BCC modifications in terms of the volumes of their unit cells (VFCC and VBCC) is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An element exists in two crystallographic modifications with FCC and BCC structures. The ratio of the densities of the FCC and BCC modifications in terms of the volumes of their unit cells (VFCC and VBCC) is?.
An element exists in two crystallographic modifications with FCC and BCC structures. The ratio of the densities of the FCC and BCC modifications in terms of the volumes of their unit cells (VFCC and VBCC) is? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about An element exists in two crystallographic modifications with FCC and BCC structures. The ratio of the densities of the FCC and BCC modifications in terms of the volumes of their unit cells (VFCC and VBCC) is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An element exists in two crystallographic modifications with FCC and BCC structures. The ratio of the densities of the FCC and BCC modifications in terms of the volumes of their unit cells (VFCC and VBCC) is?.
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