Question

# 9. In Question 1, it was noted that the net bonding energy En between two isolated positive and negative ions is a function of interionic distance r as follows: E_{N}=-\frac{A}{r}+\frac{B}{r^{n}}

where A, B, and n are constants for the particular ion pair. This equation is also valid for the bonding energy between adjacent ions in solid materials. The modulus of elasticity "E" is proportional to the slope of the interionic force-separation curve at the equilibrium interionic separation that is is E =kx(df/dr) Derive an expression for the dependence of the modulus of elasticity on these A, B, and n parameters (for the two-ion system) using the following procedure: \text { a. Establish a relationship for the force } \mathrm{F} \text { as a function of } \mathrm{r} \text {, realizing that } F=\frac{d E_{N}}{d \mathbf{r}} b. Now take the derivative dF/dr. c. Substitute the value of ro obtained in Question 1 in the above expression and determine the expression for the modulus of elasticity “E". [Assume k = 2]

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