See the attached file.
3. A plot of the lattice energies for MCI; salts for M = Ca to Zn and a drawing of the cell are shown to the right. In the electrostatic model for "ionic bonding" U is proportional to (Z+)(Z-)e2A/(r+ + r.) where Z+ and Z- are the ion charges, A is the structure (Madelung) constant and r+ + r are the radii of the ions (see p. 88 of the text for more on this). Since the radius of the cation should decrease systematically as the effective number charge increases on going across the fourth row, one might expect a similar smooth variation in the lattice energy. Clearly, this is not the case. Provide an explanation for the observed variation in lattice energy that accounts for the fact that the points for Ca2+, Mn2+ and Zn2+ deﬁne a nearly straight line that would appear to be consistent with the expected gradual decrease in their radii, whereas the other elements have somewhat greater lattice energies than predicted on this basis. The graph is in attachment.

4. Use the experimentally determined values for Delta 0 for V2+ in solid VCl2; (9200 cm") and Ni2+ in solid NiCl2 (6920 cm-1) to support your explanation for the phenomena described in problem 3. This requires calculations of LFSE; example problem 20.3 will provide guidance for those who need help. Estimate the actual deviation in lattice energies from the predicted value based on the line connecting the values for Ca2+, Mn2+ and Zn2+ in the ﬁgure. The diagram is in the attachment.
from problem 3.

See the attached file.
Solutions:
3. The lattice energy is the enthalpy change required to convert one mole of solid into its constituent gaseous ions, i.e. MCl2 (s) → M2+ (g) + 2Cl- (g)
As the size of M2+ gets smaller, the charge density increases, so a gradual or smooth variation in lattice energy is expected.

If there was no such thing as crystal field theory, we'd expect the given graph to follow the dashed line, increasing regularly from Ca2+ (which doesn't have any d-electrons) to Zn2+ (which has d10 configuration). But that is not the case! Some M2+ lattice energies lie above the line, which means that these complexes are more stable than we would expect.

Hello:
I need help understanding the relationship (if any) of the latticeenergy of compounds such as ZnO vs. H3BO3 vs. their respective solubilities.
For instance, at neutral pH and standard conditions, I'm trying to understand why ZnO is much much less soluble in water than is H3BO3 --- is it possible because of a differ

State which compound in each of the following pairs of ionic substances has the most exothermic latticeand why:
NaCl, CaS
Li2O, Na2O
LiF, NaCl
MgO, CaS
Plus two requirements that should be satisfied for a molecule to be polar

I'm having trouble understanding the concept of "nearest neighbours" and "next nearest neighbours." I understand that the number of nearest neighbours is the number of atoms per unit cell, but that's all I know (and I'm not sure why).
I'd like someone to show me how to calculate the number of nearest, second nearest, third

Look at the dissolution of various salts. Compare the dissolution of sodium hydroxide with that of sodium chloride. a) How do the energy changes for the overall processes compare?
b) Discuss the difference in magnitude of each of the three steps for dissolution of the two compounds.

In most metals, the atomic ions form a regular arrangement called a crystal lattice. The conduction electrons in the sea of electrons move through this lattice. The figure below is a one-dimensional model of a crystal lattice. The ions have mass m, charge e, and an equilibrium separation b.
a) Suppose the middle charge is d

What is meant by the terms: (i) normal mode and (ii) phonon. Explain why phonons obey Planck-Bose/Einstein statistics. What is the difference between an acoustic mode, and optic mode?
Quantized lattice vibrations are called phonons. When a phonon propagetes to a crystal lattice the atomic oscillators excited and vibrate as pe

Please see the attached file for further details.
9.23
Specify which compound in the following pairs of ionic compounds has the higher latticeenergy: (a) KCI or MgO, (b) LiF or LiBr, (c) or NaCl. Explain your choice. See attachment.
9.24
Compare the stability (in the solid state) of the following pairs of compounds:

See attached file for more details.
1. A plane wave in incident upon single atom regular lattice. Calculate the scattered amplitude from all the atoms.
2. For the unit cell vectors given, find the value of alpha, beta and gamma where maximal diffraction will be observed.
3. Define the Brillouin zone and demonstrate that

Consider a lattice of N particles in an external homogeneous magnetic field,
where each particle has two possible energy states, depending on whether the spin of the particle points in the direction of the magnetic field ("down") or opposite to it ("up"). In the "down" state the particle has no energy e = 0 and in the "up" s