Vidaara.orgClass 12 · Chemistry
CodeVID-C12-01-T2-01
Assignment — Packing, Density & Voids
Name: ____________________
Roll No.: __________
Date: ____________
General Instructions
- All questions are compulsory.
- Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
- Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions
5 × 1 = 5 marks
1.
The coordination number in both hcp and ccp is:
- A.6
- B.8
- C.12
- D.4
2.
The stacking sequence of hcp is:
- A.ABCABC
- B.ABAB
- C.AAAA
- D.ABACAB
3.
Packing efficiency of bcc is:
- A.52.4%
- B.68%
- C.74%
- D.60%
4.
The radius ratio $r/R$ for an octahedral void is:
- A.0.225
- B.0.414
- C.0.732
- D.0.155
5.
In the density formula, $N_A$ stands for:
- A.atomic number
- B.Avogadro's number
- C.mass number
- D.number of voids
Section B — Short Answer (2 marks)
3 × 2 = 6 marks
6.
State the edge–radius relations for simple cubic, bcc and fcc lattices.
7.
How many tetrahedral and octahedral voids are present for $N$ close-packed atoms?
8.
Write the formula for the density of a unit cell and define each term.
Section C — Short Answer (3 marks)
2 × 3 = 6 marks
9.
An element crystallises in fcc with $a=409\ \text{pm}$ and $M=108\ \text{g/mol}$. Find its density.
10.
Derive the packing efficiency of an fcc lattice (74%).
Section D — Long Answer (5 marks)
1 × 5 = 5 marks
11.
Describe hcp and ccp close packing (stacking, coordination number). Define tetrahedral and octahedral voids with their numbers, and derive the density formula for a unit cell.
Answer Key
Section A — Multiple Choice Questions
- (C) 12
- (B) ABAB
- (B) 68%
- (B) 0.414
- (B) Avogadro's number
Section B — Short Answer (2 marks)
- Simple cubic $a=2r$; bcc $\sqrt{3}\,a=4r$; fcc $\sqrt{2}\,a=4r$.
- Tetrahedral voids $=2N$ and octahedral voids $=N$.
- $d=\frac{zM}{a^3 N_A}$: $z$ = atoms per cell, $M$ = molar mass, $a$ = edge length, $N_A$ = Avogadro's number.
Section C — Short Answer (3 marks)
- $d=\frac{4\times108}{(4.09\times10^{-8})^3\times6.022\times10^{23}}\approx10.5\ \text{g cm}^{-3}$ (silver).
- For fcc, $z=4$ and $\sqrt{2}a=4r$ so $r=\frac{a}{2\sqrt{2}}$; efficiency $=\frac{4\times\frac{4}{3}\pi r^3}{a^3}=\frac{\pi}{3\sqrt{2}}=0.74=74\%$.
Section D — Long Answer (5 marks)
- hcp repeats ABAB, ccp/fcc repeats ABCABC; both have coordination number 12 and 74% efficiency. For $N$ spheres there are $2N$ tetrahedral and $N$ octahedral voids. Density: mass of cell $=\frac{zM}{N_A}$, volume $=a^3$, so $d=\frac{zM}{a^3 N_A}$.
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