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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
A unit cell of iron crystal has edge length 288 pm and density 7.86 g.cm-3. Find the number of atoms per unit cell and type of the crystal lattice.
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Gold occurs as face centred cube and has a density of 19.30 kg dm-3. Calculate atomic radius of gold. (Molar mass of Au = 197)
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Explain how much portion of an atom located at (i) corner and (ii) body-centre of a cubic unit cell is part of its neighbouring unit cell.
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Explain with reason sign conventions of ΔS in the following reaction
N2(g) + 3H2(g) → 2NH3(g)
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The density of silver having an atomic mass of 107.8 g mol- 1 is 10.8 g cm-3. If the edge length of cubic unit cell is 4.05 × 10- 8
cm, find the number of silver atoms in the unit cell.
( NA = 6.022 × 1023, 1 Å = 10-8 cm)
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The number of atoms per unit cell in a body centered cubic structure is ____________.
An element forms a cubic unit cell with edge length 405 pm. Molar mass of this element is 2.7 × 10−2 kg/mol and its density is given as 2.7 × 103 kg/m3. How many atoms of these elements are present per unit cell?
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An element (atomic mass 100 g/mol) having bcc structure has unit cell edge 400 pm. The density of element is (No. of atoms in bcc, Z = 2).
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Edge length of unit cell of chromium metal is 287 pm with a bcc arrangement. The atomic radius is of the order:
The edge length of fcc cell is 508 pm. If the radius of cation is 110 pm, the radius of anion is:
An element with atomic mass 100 has a bcc structure and edge length 400 pm. The density of element is:
Match the type of unit cell given in Column I with the features given in Column II.
| 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. |
| (iii) Face centred cubic unit cell | (c) Each of the three perpendicular edges compulsorily have the same edge length i.e; a = b = c. |
| (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. |
The correct set of quantum numbers for 3d subshell is
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The correct set of quantum numbers for 2p sub shell is:
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