Question

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1.Energetics of diatomic systems II.

An approximate expression for the potential energy of two

ions as a function of their separation is

PE

= −ke2r+br9 (1)

The first term is the usual Coulomb interaction,while the second term is introduced to account for

the repulsive effect of the two ions at smalldistances.

(a) Find b as a function of the equilibrium

spacing ro. (b) Calculate the potentialenergy of KCl at its equilibrium spacing (ro =0.279 nm)

2.Energetics of diatomic systems III. An expression forthe potential energy of two neutral atoms

as a function of their separation

r is given by the Morse potential,

PE

= Poh1 − e−a(r−ro)i2 (2)

(a)

Show that ro is the atomic spacing and Po the dissociation energy.(b) Calculate the force

constant for small oscillations about r=ro.

3.Crystal lattice energy. Consider a one-dimensionalchain of alternating positive and negative

ions. Show that the potential energy associatedwith one of the ions and its interactions with the

rest of this hypothetical crystal is

U

(r) = −kee2r(4)

where the Madelung constant is

=2 ln 2 and r is the interionic spacing.