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प्रश्न
How many atoms constitute one unit cell of a face-centered cubic crystal?
How many atoms are present per unit cell in a face-centred cubic system?
In a face-centred arrangement of atoms of an element, what will be the numbers of atoms present in respective unit cells? Justify your answer with calculation.
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उत्तर
The cubic unit cell in face-centred cubic systems is made up of one atom at each of the cube’s eight corners and atoms at the centre of each of the cube’s six faces. Eight unit cells share each corner atom evenly, contributing 1/8 of the unit cell. Two unit cells share equally each atom located in the centre of the face, contributing half of the two unit cells.
∴ Number of atoms in a face-centred unit cell = `(8 xx 1/8) + (6 xx 1/2)`
= 1 + 3
= 4 atoms
Thus, the unit cell of a face-centred cubic system contains 4 atoms.
संबंधित प्रश्न
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| Column I | Column II |
| (i) Primitive cubic unit cell | (a) Each of the three perpendicular edges compulsorily have the different edge length i.e; a ≠ b ≠ c. |
| (ii) Body centred cubic unit cell | (b) Number of atoms per unit cell is one. |
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| (iv) End centred orthorhombic cell | (d) In addition to the contribution from unit cell the corner atoms the number of atoms present in a unit cell is one. |
| (e) In addition to the contribution from the corner atoms the number of atoms present in a unit cell is three. |
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