(Model answers will be posted shortly after the due date.)

Question 2.12

Calculate the force of attraction between a Ca²⁺ ion and an O^2- ion, the centres of which are 1.25 nm apart.

Question 2.13

The net potential energy between two adjacent ions may be represented as

E= - A/r + B/rⁿ (2.11)

Calculate the bonding energy E₀ in terms of the parameters A, B, and n, using the following procedure:

1. Differentiate E with respect to r and set the resulting expression equal to zero.
2. Solve for r₀, the equilibrium interatomic spacing, in terms of A, B and n.
3. Obtain an expression for E₀ by substituting r₀ into Equation 2.11.

Question 2.16

The net potential energy E_N between two adjacent ions is sometimes represented by the expression

E = - C/r + D exp(-r / p) (2.12)

where r is the interionic separation, and C, D and p are constants depending on the specific ions.

1. Derive an expression for the bonding energy E₀ in terms of the equilibrium ionic separation r₀ and the constants D and p, using the following procedure:
   1. Differentiate E with respect to r and set the resulting expression equal to zero.
   2. Solve for C, in terms of D, p and r₀, the equilibrium interionic spacing.
   3. Obtain an expression for E₀ by substituting for C in Equation 2.12.

2. Now derive another expression for E₀ in terms of r₀ and the constants C and p, using similar means.

Question 3.2

What is the difference between a crystal structure and a crystal system?

Question 3.11

Some hypothetical metal has a simple cubic crystal structure. If its atomic weight is 74.5 grams/mol and its atomic radius is 0.145 nanometres, calculate its density.

Question 3.14

Niobium has an atomic radius of 0.143 nm and a density of 8.57 grams per cubic centimeter. Determine whether it has a FCC or BCC crystal structure.

Question 3.48

1. Derive planar density expressions for the BCC (100) and (110) planes in terms of the atomic radius R.
2. Compute and compare planar density values for these same two planes for molybdenum.