DVOD
The density of cubic lattice of Ag metal is 10.59/cm3 and length of its
unit cell is 4.0862 x 10-8cm then find numbers of Ag atoms in a unit cell
(Ag = 108 g/mole)
Answers
Answer:Density of Unit Cell
3
A
Z M d
a N d = Density (g/cm3
)
Z = number of atoms per unit cell a = Edge length in cm
Value of z for M = Molar mass in g/mol
simple cubic lattice = 1 NA
= Avogadro constant in per mol
bcc lattice = 2
ccp or fcc lattice = 4
Radius Ratio : It is the ratio of radius of cation to the radius of anion.
radius ratio
r
r
S.No. Radius Ratio C.N. Type of void or hole Example
1. 0.155 – 0.225 3 Trigonal planar B2O3
2 0.225 – 0.414 4 Tetrahedral ZnS
3 0.414 – 0.732 6 Octahedral NaCl
3 0.732 – 1.000 8 Cubic CsCl
Relationship between atomic radius and edge length.
Simple Cubic BCC FCC 2
a
r 3
4
a
r 2
4
a
r
In ccp or hcp packing two types of voids namely (i) tetrahedral (ii) octahedral are generated.
No. of octahendral voids present in a lattice = Number of close packed particles
No. of tetrahedral voids present in a lattice = 2 × number of close packed particles
In ionic solids, the larger ions (usually anions) form close packed structure and the smaller
ions (usually cations) occupy voids. If the cation is small enough then tetrahedral voids are occupied,
if bigger, then octahedral voids. Not all octrahedral or teterahedral voids are occupied. The fraction
of octahedral or tetrahedral voids that are occupied, depends upon the chemical formula of the
compound.
2 Chemistry
Imperfections in Crystals
Schottky Defects
Cations and equal number of anions are missing from the lattice site of a crystal of the type
A+ B– e.g., there are 106
schottky pairs per cm3
at room temperature of NaCl. Schottkey defect
lowers the density of crystal. Ionic substances showing schottky defects have almost similar sizes
of cations and anions, e.g.; NaCl, KCl, KF, etc.
Frenkel Defects
Cation is missing from the lattice site but trapped within interstitial position, e.g., Ag Br,
AgCl, Agl, AnS, etc. where cations and anions have much difference in their sizes, show this type
of defect.
F-Centre
Anions are missing from lattice sites and these anionic sites are occupied by unpaired electrons.
Anionic sites occupied by unpaired electrons are called F-centres and are responsible for colour
imparted to crystals.
Metal Deficiency Defect
Some metal oxides contain less amount of metal as compared to the stoichiometric proportion.
In iron oxide of composition Fe0.95.O, some Fe2+ are replaced by definite number of Fe3+ resulting
in the metal deficiency.
Packing Efficiency
It is the percentage of total space filled by particles.
Packing efficiency
hcp and ccp 74%
BCC 68%
Simple cubic lattice 52.4%
Explanation: