QUESTION

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1. Given: (a) The potential energy $U$ of the two atoms a distance $r$ apart. (b) $\mathrm{m}=11, \mathrm{n}=5$. (c) The equilibrium position between two atoms, $\mathrm{r}_{0}=0.31 \mathrm{~nm}$. (d) Minimum energy is $U_{\min }=-5.5 \mathrm{eV}$. Find: (i) A and B? (ii) Elastic modulus $\mathrm{E}$ around $\mathrm{r}_{0}$ ? (iii) Use the Taylor theorem to expand the potential energy around $r=r_{0}$, and compare the differences between second-order and third-order approximation for the elastic modulus. (iv) Find maximum force that can break the bond. (v) Find the work done to completely separate the two atoms from their equilibrium position. (vi) Show that when $m<n$ the system is unstable. \[ U(r)=-\frac{A}{r^{n}}+\frac{B}{r^{m}} \]

Public Answer

HSZOUM The First Answerer