Question

Match the mineral names in Group I with corresponding space groups in Group II.

Group-I	Group-II
P. Diamond	1. P63/mmc
Q. Coesite	2. R\(\bar{3}\)c
R. Graphite	3. Fd\(\bar{3}\)m
S. Calcite	4. C2/c

• A. P-4; Q-2; R-3; S-1
• B. P-1; Q-3; R-2; S-4
• C. P-3; Q-4; R-1; S-2
• D. P-2; Q-1; R-4; S-3

Hint:

Diamond and graphite are both pure carbon but differ in symmetry: diamond is cubic (Fd3m), graphite is hexagonal (P63/mmc). Calcite is trigonal, coesite is monoclinic.

Answer 1

The Correct Option is C

Step 1: Recall the crystal system and space group of each mineral.
Every mineral has a fixed atomic arrangement, and this arrangement is described by a space group symbol that combines a crystal system, a lattice type, and the symmetry elements present. We take each of the four minerals in turn.

Step 2: Diamond (P).
Diamond crystallises in the cubic system with a face centred lattice, and each carbon atom sits at the centre of a tetrahedron of four other carbon atoms. Its space group is
\[ Fd\bar{3}m \]
So P matches with option 3.

Step 3: Coesite (Q).
Coesite is a high pressure polymorph of silica, \(SiO_2\), stable at pressures well above those where quartz forms, and it crystallises in the monoclinic system. Its space group is
\[ C2/c \]
So Q matches with option 4.

Step 4: Graphite (R).
Graphite is built of stacked hexagonal sheets of carbon atoms held together by weak forces between the layers, giving it a hexagonal crystal system. Its space group is
\[ P6_3/mmc \]
So R matches with option 1.

Step 5: Calcite (S).
Calcite, \(CaCO_3\), crystallises in the trigonal system with rhombohedral symmetry. Its space group is
\[ R\bar{3}c \]
So S matches with option 2.

Step 6: Put the pairs together and check the options.
We now have P-3, Q-4, R-1, S-2.

(A) P-4; Q-2; R-3; S-1: Wrong, it swaps diamond and coesite's groups and misassigns graphite and calcite too.

(B) P-1; Q-3; R-2; S-4: Wrong, it gives diamond the graphite space group and graphite the calcite space group.

(C) P-3; Q-4; R-1; S-2: Matches our derivation exactly. Correct.

(D) P-2; Q-1; R-4; S-3: Wrong, none of these four pairs is right; it looks like a completely shifted set.

Step 7: Final conclusion.
\[ \boxed{P\text{-}3;\ Q\text{-}4;\ R\text{-}1;\ S\text{-}2} \]
Hence, the correct option is (C).