Question

1) The net potential energy between two adjacent ions, EN, may be represented by:

En = Ea + Er, where Ea = (-A/r) and Er = (b/r^n)

a) Provide a brief explanation as to why the interionic separation, r0, is obtained when dEN/dr = 0.

b) Using the condition discussed in part (a), differentiate EN with regards to r in order to derive the following expression for the interionic separation:

r0 = (A/nB)^(1/(1-n))

c) Using the expression, you derived in part (b) and the original expression for EN, provide an equation expressing the corresponding bonding energy, E0.

d) The interionic separation of potassium fluoride, KF, is 0.269 nm, with a corresponding bonding energy of 8.23 eV. If the value of n is 5, use the expressions you derived in part (b) and part (c) to determine constants A and B to give an explicit expression for EN in terms of r. Note: do not convert any of the units.

Answer 1