3 free questions from this chapter (the full set has 30). Marking: Multi-correct: +4 all correct, +1 per correct option if none wrong, −2 if any wrong · Numerical: +4 / 0 · Matching: +3 / −1.
Question 1Level 2 · ExamSingle correct
A cubic metal (M=55.85 g mol−1) has edge length a=286.65 pm and density 7.874 g cm−3. Treat atoms/ions as hard spheres; NA=6.022×1023mol−1; 1pm=10−10 cm. The lattice type and the atomic radius of the metal are ______. Exactly one option is correct.
ASimple cubic; 143.3 pm
BBody-centred cubic; 124.1 pm
CFace-centred cubic; 101.3 pm
DFace-centred cubic; 124.1 pm
Show answer and solution
Answer: B
Z=ρNAa3/M=7.874×6.022×1023×(286.65×10−10)3/55.85=2.00, so the cell is body-centred cubic. In bcc the atoms touch along the body diagonal: 4r=3a, so r=3(286.65)/4=124.1 pm. Option C uses the fcc relation r=a/(22)=101.3 pm; option A uses the simple-cubic relation r=a/2=143.3 pm. Answer: B.
Difficulty: Hard
Question 2Level 3 · AdvancedSingle correct
Lithium iodide adopts the rock-salt (NaCl-type) structure: I− ions at fcc positions and Li+ ions in all octahedral voids. Take r(Li+)=76 pm and r(I−)=220 pm and treat both as incompressible hard spheres. The crystal adopts the smallest cubic edge length a for which no two spheres overlap. The value of a and the type of contact that fixes it are ______. Exactly one option is correct.
A592 pm; Li+-I− contact along the cell edge
B592 pm; I−-I− contact along the face diagonal
C622.3 pm; I−-I− contact along the face diagonal, Li+ not touching I−
D622.3 pm; Li+-I− contact along the cell edge
Show answer and solution
Answer: C
Two conditions must both hold. (i) No cation-anion overlap along an edge: a≥2(r++r−)=592 pm. (ii) No anion-anion overlap along a face diagonal (I− ions at fcc positions, nearest I−-I− distance a/2): a/2≥2r−, i.e. a≥22r−=622.3 pm. The smallest allowed a is the larger value, 622.3 pm, fixed by I−-I− contact.
Insight: r+/r−=76/220=0.345<0.414, so Li+ is too small for the octahedral void. It "rattles" in the void without touching the I− ions, and the anion framework sets the cell size. Using a=2(r++r−) would push the I− ions into each other. Answer: C.
Difficulty: Peak challenge
Question 3Level 3 · AdvancedSingle correct
Using the conventional cell parameters a,b,c,α,β,γ (α is the angle between b and c, β between a and c, γ between a and b), the correct combination of crystal system, parameters and possible Bravais lattices is ______. Exactly one option is correct.
AMonoclinic: a=b=c, α=γ=90∘=β; primitive and end-centred lattices
BRhombohedral: a=b=c, α=β=γ=90∘; primitive lattice only
CTetragonal: a=b=c, α=β=γ=90∘; primitive, body-centred and face-centred lattices
DHexagonal: a=b=c, α=β=90∘, γ=60∘; primitive and end-centred lattices
Show answer and solution
Answer: A
A: Monoclinic has a=b=c, α=γ=90∘=β, and two Bravais lattices: primitive and end-centred. Correct.
B: Rhombohedral has a=b=c but α=β=γ=90∘. With all angles 90∘ the cell would be cubic. Wrong.
C: Tetragonal has only primitive and body-centred lattices. A face-centred tetragonal cell can be redrawn as a smaller body-centred tetragonal cell. Wrong.
D: Hexagonal has γ=120∘ and only one (primitive) Bravais lattice. Wrong.
Answer: A.
Difficulty: Very hard
Get the full chapter for ₹99
Timed attempt with real exam marking, your rank among everyone who took it, solutions for every question, and spaced revision of your mistakes.