UPSC Combined Geo-Scientist, Mains · 2025 · Mains Paper II
Q1(d). Symmetry elements of orthorhombic Mg₂SiO₄
Question
Mg₂SiO₄ crystallizes in an orthorhombic crystal system. What are the maximum and minimum symmetry elements it can possess?
Answer in brief
Maximum (class mmm): three 2-fold axes + three mirror planes + a centre of symmetry. Minimum (class 222): three mutually perpendicular 2-fold axes.
Key points
- Orthorhombic point groups: 222 (D₂), mm2 (C₂ᵥ) and mmm (D₂ₕ). No axis higher than 2-fold.
- Minimum (essential symmetry): three mutually perpendicular 2-fold axes.
- Maximum (holohedral class mmm): 3C₂ + 3m + i = 7 elements.
- Forsterite (olivine) belongs to class mmm, space group Pbnm. It shows the maximum.
The full model answer
As written for the answer booklet: the diagram carries the working, the lines stay short. Read here only; it is not offered as a download.
Coversorthorhombic crystal systemsymmetry elementspoint group mmmforsteritecrystal classes
All parts of Question 1
- 1(a) Why Z > 1 for H₂ and He at all pressures5 marks
- 1(b) Corresponding state of H₂S for N₂ at 25 °C and 1 atm5 marks
- 1(c) Band structure of n-type and p-type semiconductors5 marks
- 1(d) Symmetry elements of orthorhombic Mg₂SiO₄5 marks
- 1(e) Fall of G with temperature at constant pressure5 marks
- 1(f) Z > 1 and f > P for the gas P(Vm − b) = RT5 marks
- 1(g) Overall equation and the role of each species5 marks
- 1(h) log k against pH for specific H⁺ catalysis5 marks
- 1(i) KCl salt bridge for a silver–lead cell5 marks
- 1(j) Equilibrium constant from standard potentials5 marks
- 1(k) Conditions for an acceptable wave function5 marks
- 1(l) No solution with E = 0 for the particle in a box5 marks
- 1(m) Discrete levels and the resonance condition5 marks
- 1(n) Rotational activity of CO and CO₂5 marks
- 1(o) Measuring light intensity with a chemical actinometer5 marks
- 1(p) Why watch hands glow in the dark5 marks