Q.What is the co-ordination number of particles present in FCC crystal structure ?
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Coordination Number: The "How Many Neighbours" Rule
Imagine you are standing in a crowded room. The people closest to you — the ones you could touch without moving your feet — are your immediate neighbours. Now imagine that same idea, but inside a crystal. Atoms or ions don't float around randomly; they pack together in repeating patterns. The coordination number (CN) is simply the count of those immediate neighbours that touch a given atom or ion.
It answers one question: How many nearest neighbours does this particle have?
The Intuition: Packing and Touching
Think of stacking oranges at a fruit market. If you arrange them in a single flat layer, each orange touches six others around it (like a honeycomb). That's a coordination number of 6 for that layer. But if you stack a second layer on top, each orange now also touches three oranges above and three below — so the total nearest neighbours become 12. The coordination number changes depending on how the oranges are stacked.
In a crystal, the coordination number is determined by two things:
- The size of the atoms/ions (can a smaller ion fit more neighbours around it?)
- The geometry of the arrangement (cubic, hexagonal, etc.)
A higher coordination number means the atom is more tightly surrounded — it's "more crowded" in a sense, but also more stable energetically.
The Precise Definition
Coordination Number (CN) = The number of nearest-neighbour atoms or ions that are in direct contact with a given atom or ion in a crystal lattice.
"Nearest neighbour" means the shortest distance between centres of two particles in the lattice. These neighbours are touching — not just close, but physically adjacent.
Common Examples You Must Know
| Crystal Structure | Coordination Number | Arrangement |
|---|---|---|
| Simple Cubic (SC) | 6 | One atom at each corner of a cube; neighbours are left, right, front, back, top, bottom |
| Body-Centred Cubic (BCC) | 8 | Atom at centre touches all 8 corner atoms |
| Face-Centred Cubic (FCC) | 12 | Atom at a face centre touches 4 atoms in its own face, 4 in the adjacent face, and 4 more |
| Hexagonal Close-Packed (HCP) | 12 | Similar to FCC — each atom touches 6 in its own layer, 3 above, 3 below |
| NaCl (rock salt) | 6 (for each ion) | Each Na⁺ is surrounded by 6 Cl⁻ ions (octahedral) |
| CsCl | 8 (for each ion) | Each Cs⁺ is surrounded by 8 Cl⁻ ions (cubic) |
Do not confuse coordination number with the number of atoms per unit cell. For example, in BCC, the unit cell contains 2 atoms, but the coordination number is 8. These are different concepts.
Why Does It Matter?
Coordination number directly affects physical properties:
- Melting point: Higher CN usually means stronger bonding → higher melting point.
- Density: Tighter packing (higher CN) often means denser material. …
In a close-packed FCC (ccp) lattice, each particle touches nearest neighbours both within its own layer and in the layers directly above and below it, and counting these gives its co-ordination number.
…
In a face-centred cubic (FCC/ccp) lattice, each particle touches 12 nearest neighbours, giving a co-ordination number of 12.
In an FCC unit cell, lattice points lie at the 8 corners and at the centre of each of the 6 faces. Consider any one particle, say the one at a face-centre: it touches 4 corner particles in its own layer, 4 particles in the layer directly above, and 4 particles in the layer directly below — a total of 4 + 4 + 4 = 12 nearest neighbours.
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- CBSE 2023Set F1 markMCQQ.The coordination number of a metal crystallizing in a hexagonal close packed structure is(a) 5(b) 4(c) 8(d) 12
›Reveal solutionSolution
Both hcp and ccp are close-packed with coordination number 12.
In a close-packed structure each sphere is surrounded by 6 spheres in its own layer, 3 in the layer above and 3 in the layer below, giving 6 + 3 + 3 = 12 nearest neighbours. Therefore the coordination number of a metal …
- CBSE 2022Set HE2181 markMCQQ.Which compound has 8:8 coordination number?(a) MgO(b) Al2O3(c) CsCl(d) NaCl
›Reveal solutionSolution
CsCl crystallises in a body-centred-cubic-type arrangement where each ion touches 8 oppositely charged ions, giving 8:8 coordination; NaCl, MgO and Al2O3 do not.
The coordination number in an ionic solid depends mainly on the radius ratio (r+/r-) of the cation to the anion, since it is the packing geometry that keeps oppositely charged ions in contact while like-charged ions stay apart.
- NaCl and MgO both adopt the rock-salt structure: each cation is surrounded by 6 anions and each anion by 6 cations (6:6 coordination), because their radius ratio falls in the 0.414-0.732 range (octahedral holes).
- Al2O3 (corundum-type) has a more complex structure with Al3+ in octahedral sites, again not 8:8. …
- CBSE 2022Set ANNUAL1 markQ.A compound formed by elements A and B has the A atoms forming a ccp lattice and the B atoms occupy half of the tetrahedral voids. What is the co-ordination number of B atoms in the crystal ?
›Reveal solutionSolution
B sits inside the tetrahedral voids of A's ccp lattice, so B is surrounded by 4 A atoms — coordination number 4.
In a cubic close packed (ccp/fcc) arrangement of A atoms, two kinds of voids are created between the layers: octahedral voids (surrounded by 6 nearest atoms) and tetrahedral voids (surrounded by 4 nearest atoms, arranged at the corners of a tetrahedron around the void). A ccp lattice of N atoms generates N octahedral voids and 2N tetrahedral voids.
…
- CBSE 2019Set HE1 markMCQQ.If the coordination number of cesium ion Cs+ in Cesium chloride is 8, then the coordination number of chloride ion will be -(a) 8(b) 4(c) 6(d) 12
›Reveal solutionSolution
In CsCl, Cs⁺ and Cl⁻ occupy a body-centred-cubic-type arrangement in which each ion is surrounded by 8 ions of the other kind, so the coordination number of Cl⁻ is also 8.
CsCl crystallises with Cl⁻ ions at the eight corners of a cube and the Cs⁺ ion at the body centre (equivalently, either ion can be taken at the corners with the other at the centre). Each corner ion is simultaneously shared by 8 such cubes, and the ion at the body centre touches all 8 corner ions.
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- CBSE 2018Set ANNUAL1 markQ.What is the co-ordination number of particles present in FCC crystal structure ?
›Reveal solutionSolution
In a face-centred cubic (FCC/ccp) lattice, each particle touches 12 nearest neighbours, giving a co-ordination number of 12.
In an FCC unit cell, lattice points lie at the 8 corners and at the centre of each of the 6 faces. Consider any one particle, say the one at a face-centre: it touches 4 corner particles in its own layer, 4 particles in the layer directly above, and 4 particles in the layer directly below — a total of 4 + 4 + 4 = 12 nearest neighbours.
…
- CBSE 2018Set ANNUAL1 markMCQQ.The co-ordination number of a metal crystallizing in hexagonal close packed (hcp) structure is -(a) 12(b) 8(c) 4(d) 6
›Reveal solutionSolution
hcp is a close-packed structure → coordination number 12.
Both hcp and ccp are close-packed with maximum packing; each sphere is surrounded by 6 neighbours in the sa …
- CBSE 2016Set ANNUAL1 markQ.What are the coordination numbers of Na+ and Cl− in NaCl?
›Reveal solutionSolution
NaCl adopts a face-centred cubic (rock-salt) lattice in which both ions have coordination number 6.
In crystalline NaCl, Cl− ions occupy an fcc lattice and Na+ ions occupy all the octahedral voids of that lattice (or vice versa — the two sub-lattices are equivalent, each fcc, interpenetrating). Every Na+ ion is surrounded by 6 nearest-neighbour Cl− ions positioned octahedrally around it, and by symmetry every Cl− ion is l …
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