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In a fcc lattice, atom A occupies the corner position and atom B occupies the face centre position. If one atom of B is missing from one of the face centred points, the formula of the compound is:
- a)A2B5
- b)A2B
- c)A2B
- d)A2B3
Correct answer is option 'A'. Can you explain this answer?
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In a fcc lattice, atom A occupies the corner position and atom B occup...
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In a fcc lattice, atom A occupies the corner position and atom B occup...
Explanation:
FCC Lattice Structure:
- FCC stands for Face-Centered Cubic.
- In an FCC lattice, the atoms are arranged in a cubic structure, with atoms on the corners and face centers of the unit cell.
- The coordination number of each atom in an FCC lattice is 12, which means that each atom is surrounded by 12 nearest neighbors.
Atom Arrangement:
- In this scenario, atom A occupies the corner position and atom B occupies the face center position in the FCC lattice.
- This means that each face of the cube has one atom of type B.
Missing Atom:
- One atom of type B is missing from one of the face-centered points.
- This means that there are only 7 atoms of type B instead of the usual 8.
Determining the Formula:
- To determine the formula of the compound, we need to find the ratio of atoms A and B.
- Since there is one atom of type A at each corner and 8 corners in total, the total number of atoms of type A is 8.
- Similarly, since there are 7 atoms of type B, we can write the ratio of A to B as 8:7.
Simplifying the Ratio:
- To simplify the ratio, we can divide both numbers by their greatest common divisor, which is 1 in this case.
- Dividing 8 by 1 gives 8, and dividing 7 by 1 gives 7.
- Therefore, the simplified ratio of atoms A to B is 8:7.
Writing the Compound Formula:
- The formula of the compound is written by combining the symbols of the elements in the ratio determined above.
- Since atom A is the dominant element, it is written first, followed by atom B.
- The formula is written as A8B7.
Reducing the Formula:
- The formula A8B7 can be further reduced by dividing both subscripts by their greatest common divisor, which is 1 in this case.
- Dividing 8 by 1 gives 8, and dividing 7 by 1 gives 7.
- Therefore, the reduced formula of the compound is A2B5.
Conclusion:
- The formula of the compound with atom A occupying the corner position and atom B occupying the face center position, with one atom of B missing from one of the face-centered points, is A2B5.
FCC Lattice Structure:
- FCC stands for Face-Centered Cubic.
- In an FCC lattice, the atoms are arranged in a cubic structure, with atoms on the corners and face centers of the unit cell.
- The coordination number of each atom in an FCC lattice is 12, which means that each atom is surrounded by 12 nearest neighbors.
Atom Arrangement:
- In this scenario, atom A occupies the corner position and atom B occupies the face center position in the FCC lattice.
- This means that each face of the cube has one atom of type B.
Missing Atom:
- One atom of type B is missing from one of the face-centered points.
- This means that there are only 7 atoms of type B instead of the usual 8.
Determining the Formula:
- To determine the formula of the compound, we need to find the ratio of atoms A and B.
- Since there is one atom of type A at each corner and 8 corners in total, the total number of atoms of type A is 8.
- Similarly, since there are 7 atoms of type B, we can write the ratio of A to B as 8:7.
Simplifying the Ratio:
- To simplify the ratio, we can divide both numbers by their greatest common divisor, which is 1 in this case.
- Dividing 8 by 1 gives 8, and dividing 7 by 1 gives 7.
- Therefore, the simplified ratio of atoms A to B is 8:7.
Writing the Compound Formula:
- The formula of the compound is written by combining the symbols of the elements in the ratio determined above.
- Since atom A is the dominant element, it is written first, followed by atom B.
- The formula is written as A8B7.
Reducing the Formula:
- The formula A8B7 can be further reduced by dividing both subscripts by their greatest common divisor, which is 1 in this case.
- Dividing 8 by 1 gives 8, and dividing 7 by 1 gives 7.
- Therefore, the reduced formula of the compound is A2B5.
Conclusion:
- The formula of the compound with atom A occupying the corner position and atom B occupying the face center position, with one atom of B missing from one of the face-centered points, is A2B5.
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In a fcc lattice, atom A occupies the corner position and atom B occupies the face centre position. If one atom of B is missing from one of the face centred points, the formula of the compound is:a)A2B5b)A2Bc)A2Bd)A2B3Correct answer is option 'A'. Can you explain this answer?
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