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Assuming atoms to be perfect spheres, what is the value of the highest possible atomic packing factor (APF) in metals?
- a)0.95
- b)0.74
- c)0.66
- d)0.5
Correct answer is option 'B'. Can you explain this answer?
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Assuming atoms to be perfect spheres, what is the value of the highest...
Ans. (b) Packing factor = 0.74 which is maximum and for F.C.C and HCP structure.
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Assuming atoms to be perfect spheres, what is the value of the highest...
Highest possible atomic packing factor (APF) in metals is 0.74.
Explanation:
Atomic packing factor (APF) is a measure of how efficiently atoms are arranged in a crystal structure. It is the ratio of the volume occupied by atoms to the total volume of the unit cell.
In metals, atoms are closely packed together in a regular pattern. The two most common types of arrangements are face-centered cubic (FCC) and body-centered cubic (BCC) structures.
- Face-centered cubic (FCC) structure:
In an FCC structure, each corner of the cube is occupied by an atom, and there is an additional atom at the center of each face. This gives a total of 4 atoms per unit cell.
The volume occupied by atoms in an FCC structure can be calculated as follows:
Volume occupied by atoms = (number of atoms) * (volume of each atom)
= 4 * (4/3 * π * (radius of atom)^3)
= 16/3 * π * (radius of atom)^3
The total volume of the unit cell in an FCC structure is given by:
Total volume of unit cell = (length of unit cell)^3
Therefore, the atomic packing factor (APF) for an FCC structure is:
APF = (volume occupied by atoms) / (total volume of unit cell)
= (16/3 * π * (radius of atom)^3) / ((length of unit cell)^3)
- Body-centered cubic (BCC) structure:
In a BCC structure, each corner of the cube is occupied by an atom, and there is an additional atom at the center of the cube. This gives a total of 2 atoms per unit cell.
The volume occupied by atoms in a BCC structure can be calculated as follows:
Volume occupied by atoms = (number of atoms) * (volume of each atom)
= 2 * (4/3 * π * (radius of atom)^3)
= 8/3 * π * (radius of atom)^3
The total volume of the unit cell in a BCC structure is given by:
Total volume of unit cell = (length of unit cell)^3
Therefore, the atomic packing factor (APF) for a BCC structure is:
APF = (volume occupied by atoms) / (total volume of unit cell)
= (8/3 * π * (radius of atom)^3) / ((length of unit cell)^3)
Comparing the APF values for FCC and BCC structures, it can be observed that the highest possible APF is 0.74, which corresponds to the FCC structure. Therefore, the correct answer is option 'B' (0.74).
Explanation:
Atomic packing factor (APF) is a measure of how efficiently atoms are arranged in a crystal structure. It is the ratio of the volume occupied by atoms to the total volume of the unit cell.
In metals, atoms are closely packed together in a regular pattern. The two most common types of arrangements are face-centered cubic (FCC) and body-centered cubic (BCC) structures.
- Face-centered cubic (FCC) structure:
In an FCC structure, each corner of the cube is occupied by an atom, and there is an additional atom at the center of each face. This gives a total of 4 atoms per unit cell.
The volume occupied by atoms in an FCC structure can be calculated as follows:
Volume occupied by atoms = (number of atoms) * (volume of each atom)
= 4 * (4/3 * π * (radius of atom)^3)
= 16/3 * π * (radius of atom)^3
The total volume of the unit cell in an FCC structure is given by:
Total volume of unit cell = (length of unit cell)^3
Therefore, the atomic packing factor (APF) for an FCC structure is:
APF = (volume occupied by atoms) / (total volume of unit cell)
= (16/3 * π * (radius of atom)^3) / ((length of unit cell)^3)
- Body-centered cubic (BCC) structure:
In a BCC structure, each corner of the cube is occupied by an atom, and there is an additional atom at the center of the cube. This gives a total of 2 atoms per unit cell.
The volume occupied by atoms in a BCC structure can be calculated as follows:
Volume occupied by atoms = (number of atoms) * (volume of each atom)
= 2 * (4/3 * π * (radius of atom)^3)
= 8/3 * π * (radius of atom)^3
The total volume of the unit cell in a BCC structure is given by:
Total volume of unit cell = (length of unit cell)^3
Therefore, the atomic packing factor (APF) for a BCC structure is:
APF = (volume occupied by atoms) / (total volume of unit cell)
= (8/3 * π * (radius of atom)^3) / ((length of unit cell)^3)
Comparing the APF values for FCC and BCC structures, it can be observed that the highest possible APF is 0.74, which corresponds to the FCC structure. Therefore, the correct answer is option 'B' (0.74).
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