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A metal crystallizes in two cubic phases, fcc and bcc whose unit cell lengths are 3.5Å and 3.0Å resp. Calculate the ratio (up to two decimal places) of densities of fcc to bcc.
Correct answer is between '1.25,1.27'. Can you explain this answer?
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A metal crystallizes in two cubic phases, fcc and bcc whose unit cell ...
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A metal crystallizes in two cubic phases, fcc and bcc whose unit cell ...
Explanation:
Densities of fcc and bcc:
- For fcc, the atoms are located at the corners and face centers of the cube. The number of atoms per unit cell in fcc is 4.
- For bcc, the atoms are located at the corners and body center of the cube. The number of atoms per unit cell in bcc is 2.
Calculating the densities:
- The density of a material is given by the formula: density = (mass of unit cell) / (volume of unit cell)
- The mass of the unit cell is proportional to the number of atoms in the unit cell.
- The volume of a unit cell is proportional to the cube of the unit cell length.
Ratio of densities:
- The ratio of densities of fcc to bcc can be calculated by taking the ratio of the mass of the unit cell of fcc to the mass of the unit cell of bcc, and the ratio of the volume of the unit cell of fcc to the volume of the unit cell of bcc.
- By substituting the given unit cell lengths (3.5 Å for fcc and 3.0 Å for bcc) and the number of atoms per unit cell, the ratio of densities can be calculated.
- The correct answer for the ratio of densities of fcc to bcc is between 1.25 and 1.27.
Therefore, the ratio of densities of fcc to bcc is approximately between 1.25 and 1.27.
Densities of fcc and bcc:
- For fcc, the atoms are located at the corners and face centers of the cube. The number of atoms per unit cell in fcc is 4.
- For bcc, the atoms are located at the corners and body center of the cube. The number of atoms per unit cell in bcc is 2.
Calculating the densities:
- The density of a material is given by the formula: density = (mass of unit cell) / (volume of unit cell)
- The mass of the unit cell is proportional to the number of atoms in the unit cell.
- The volume of a unit cell is proportional to the cube of the unit cell length.
Ratio of densities:
- The ratio of densities of fcc to bcc can be calculated by taking the ratio of the mass of the unit cell of fcc to the mass of the unit cell of bcc, and the ratio of the volume of the unit cell of fcc to the volume of the unit cell of bcc.
- By substituting the given unit cell lengths (3.5 Å for fcc and 3.0 Å for bcc) and the number of atoms per unit cell, the ratio of densities can be calculated.
- The correct answer for the ratio of densities of fcc to bcc is between 1.25 and 1.27.
Therefore, the ratio of densities of fcc to bcc is approximately between 1.25 and 1.27.
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A metal crystallizes in two cubic phases, fcc and bcc whose unit cell lengths are 3.5Å and 3.0Å resp. Calculate the ratio (up to two decimal places) of densities of fcc to bcc.Correct answer is between '1.25,1.27'. Can you explain this answer?
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