Q3. Solid noble gases: forces, structure and holes
The elements Ne, Ar, Kr and Xe of group 18 form cubic close-packed crystalline solids at very low temperatures. Answer the following: (i) What type of bonding forces are involved in these solids? (ii) What crystal structure do they adopt? (iii) How many atoms are present in the unit cells of these solids? (iv) What is the coordination number of each atom in these structures? (v) How many tetrahedral and octahedral holes per atom are present in these crystal structures?
Answer in brief
(i) London (dispersion) forces. (ii) ccp = face-centred cubic. (iii) 4 atoms per cell. (iv) CN 12. (v) 2 tetrahedral and 1 octahedral hole per atom.
Key points
- noble-gas atoms are closed-shell and non-polar. The only attraction is the London dispersion force (instantaneous dipole–induced dipole), E∝-1/r⁶, which increases from Ne to Xe with polarisability: melting points 24, 84, 116,…
- Structure: ABCABC stacking = face-centred cubic, a=2√2 r.
- Atoms per cell: 8×18 (corners) + 6×12 (faces) =4.
- each atom touches 6 neighbours in its layer, 3 above and 3 below: 12.
The full model answer
Worked out step by step, as it should go in the answer booklet. The solution sheet follows it.
- Bonding: noble-gas atoms are closed-shell and non-polar. The only attraction is the London dispersion force (instantaneous dipole–induced dipole), E∝-1/r⁶, which increases from Ne to Xe with polarisability: melting points 24, 84, 116, 161 K. Packing is non-directional, so the structure is that of close-packed spheres.
- Structure: ABCABC stacking = face-centred cubic, a=2√2 r.
- Atoms per cell: 8×18 (corners) + 6×12 (faces) =4.
- CN: each atom touches 6 neighbours in its layer, 3 above and 3 below: 12.
- Holes: for N atoms there are N octahedral and 2N tetrahedral holes. In the fcc cell: 4 octahedral (body centre + 12 edge centres ×14) and 8 tetrahedral (inside the cell) per 4 atoms, i.e., 1 octahedral and 2 tetrahedral per atom.
He solidifies only under pressure (25 atm) as hcp; the ccp stacking of Ne to Xe has a packing fraction 0.74 and radius ratio rₕₒₗₑ/r = 0.414 (octahedral) and 0.225 (tetrahedral).
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