11. sine or sinθ= Perpendicular/ Hypotenuse=
Opposite/Hypotenuse. cosine or cosθ= Base/
Hypotenuse= Adjacent/Hypotenuse. tangent or tanθ=
Perpendicular/Base= Opposite/Adjacent.
18. For every Close packed arrangement, there is one octahedral hole and
two tetrahedral holes. The octahedral holes are larger than the
tetrahedral holes
20. A cation with a 2+ charge will make a stronger ionic bond than a cation with a 1+ charge. A larger ion makes a
weaker ionic bond because of the greater distance between its electrons and the nucleus of the oppositely charged
ion.
27. zinc blende is cubic, whereas wurtzite has a hexagonal structure.
34. Lattice energy can be defined as the energy
required to convert one mole of an ionic solid
into gaseous ionic constituents. Alternatively,
it can be defined as the energy that must be
supplied to one mole of an ionic crystal in order
to separate it into gaseous ions in a vacuum via
an endothermic process.
35. The ionic lattice is modeled as an assembly of hard elastic spheres which are compressed together by the mutual
attraction of the electrostatic charges on the ions. They achieve the observed equilibrium distance apart due to a
balancing short range repulsion.
Electrostatic potential
The electrostatic potential energy, Epair, between a pair of ions of equal and opposite charge is:
For a simple lattice consisting ions with equal and opposite
charge in a 1:1 ratio, interactions between one ion and all other
lattice ions need to be summed to calculate EM, sometimes
called the Madelung or lattice energy:
36. Repulsive term
Born and Lande suggested that a repulsive interaction between the lattice ions would be proportional to
1/rn so that the repulsive energy term, ER, would be expressed:
41. The Kapustinskii equation calculates the lattice energy UL for an ionic crystal, which is experimentally
difficult to determine. It is named after Anatoli Fedorovich Kapustinskii who published the formula in
1956.
where K = 1.20200×10−4 J·m·mol−1
d = 3.45×10−11 m
ν is the number of ions in the empirical formula,
z+ and z− are the numbers of elementary charge on the cation and anion,
respectively, and
r+ and r− are the radii of the cation and anion, respectively, in meters.