In a diamond, each carbon atom is ________ surrounded by other carbon atoms.

Question

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Correct — option (2), tetrahedrally. A carbon atom has four electrons in its outermost shell, and in diamond every one of them is used to form a covalent bond with a neighbouring carbon atom. Four bonds means four neighbours, and the four repel one another, so they arrange themselves as far apart as they can get — pointing towards the four corners of a regular tetrahedron with the central atom at its centre, the angle between any two bonds being about 109 and a half degrees. In the language of bonding this is the sp3 hybridised state of carbon, in which the one s orbital and the three p orbitals of the valence shell are mixed to give four identical orbitals directed towards the corners of a tetrahedron. What makes diamond diamond is that this arrangement is repeated without interruption. Each of the four neighbours is itself surrounded tetrahedrally by four more, and those by four more again, so the whole crystal is a single continuous three-dimensional network of covalent bonds rather than a collection of molecules held together by weaker forces. There is no such thing as a molecule of diamond; the crystal is the molecule. Every property of diamond follows from that structure and is worth deriving rather than memorising. Because breaking the crystal means breaking strong covalent bonds in every direction, diamond is the hardest naturally occurring substance and is used for cutting, drilling and grinding, and as an abrasive. Because those bonds must be broken to melt it, its melting point is extremely high. Because all four valence electrons are locked into bonds, there are no free electrons to carry current, so diamond does not conduct electricity, although it conducts heat exceptionally well through the vibration of its rigid lattice. Its high refractive index and strong dispersion are what give a cut stone its brilliance. The contrast with graphite, the other familiar allotrope of carbon, makes the point sharply: in graphite each carbon atom bonds to only three others in flat hexagonal sheets, the fourth electron is left free to move, and the sheets are held to one another by weak forces, which is why graphite is soft enough to write with, slippery enough to lubricate, and able to conduct electricity — everything that diamond is not, from the same element, because the atoms are arranged differently. Option (2) is the answer.

Why the other options are wrong — (a) A linear arrangement means an atom with two neighbours placed on opposite sides of it, at an angle of 180 degrees, and it belongs to carbon in a quite different bonding state. Carbon is linear where it is sp hybridised and forms two sigma bonds, as in acetylene, where each carbon is bonded to one hydrogen and to the other carbon through a triple bond, or in carbon dioxide, where the carbon sits between two oxygen atoms. Neither situation arises in diamond, where every carbon atom uses all four of its valence electrons on four separate single bonds and therefore has four neighbours, not two. The option is worth a moment only as a reminder that the geometry around an atom is decided by the number of things attached to it: two gives linear, three gives trigonal planar, four gives tetrahedral, and six gives octahedral.  (c) This is the most dangerous of the three wrong options, because it begins with the same syllable as the right answer and a candidate reading quickly under time pressure may take it for the word wanted. The two words belong to different vocabularies. Tetrahedral describes the shape made by four neighbours around a central atom, with bond angles of about 109 and a half degrees. Tetragonal is a term from crystallography, naming one of the seven crystal systems, in which the unit cell has two edges of equal length and a third of different length with all the angles right angles; diamond does not belong to that system at all but crystallises in the cubic system. Where the word tetragonal is used of the arrangement around an atom, in the form tetragonal planar, it means four neighbours lying in one plane at the corners of a square, which is the geometry of a complex such as the tetrachloroplatinate ion, and it is not the geometry of carbon in diamond, whose four neighbours are emphatically not coplanar. Reading the option to its end, rather than recognising its first four letters, is what separates the two.  (d) An octahedral arrangement means six neighbours placed at the corners of a regular octahedron, one above, one below and four around the middle, with bond angles of 90 degrees. Carbon cannot adopt it, and the reason is simply arithmetic: carbon has four valence electrons and belongs to the second period of the periodic table, where the valence shell can hold no more than eight electrons, so it can form four covalent bonds and no more. Six-coordination is common enough elsewhere — sulphur hexafluoride is a molecular example, and in the sodium chloride crystal every sodium ion has six chloride ions as nearest neighbours and every chloride ion six sodium ions — but those involve either an element that can expand its valence shell or an ionic lattice rather than a covalent one. A useful cross-check is that six bonds from each carbon would also make diamond's formula and its measured density impossible.

Concept: Allotropy is the existence of an element in more than one physical form in the same physical state, the forms differing in the way the atoms are joined rather than in what the atoms are, and carbon is its standard illustration. In diamond each carbon atom is sp3 hybridised and forms four single covalent bonds directed towards the corners of a tetrahedron, so the crystal is a giant covalent network extending in three dimensions; it is very hard, has a very high melting point, does not conduct electricity, and is prized as a gemstone for its refraction of light. In graphite each carbon atom is sp2 hybridised and forms three covalent bonds in a plane, producing flat sheets of linked hexagons; the fourth electron of each atom is delocalised over the sheet, which makes graphite a conductor, and the sheets are held together only by weak forces, which lets them slide over one another and makes graphite soft, greasy to the touch and useful both as a pencil lead and as a dry lubricant. The fullerenes are a third family, of which the best known is the sixty-atom molecule made of twenty hexagons and twelve pentagons arranged like a football, and graphene is a single isolated sheet of the graphite structure. The general principle that these forms illustrate is the one examiners are really testing: in a solid, the properties follow from the structure and the bonding, so hardness, melting point and electrical conductivity can all be predicted once the arrangement of the atoms is known.

State PCS 2022 Q50 — Science & Technology PYQ with Answer

State PCS 2022 Q50 — Science & Technology PYQ with Answer