Question #43536

The interatomic potential energy $U(r)$ (in $\text{J}$) of a hypothetical simple cubic crystal is modeled by the Morse potential: $U(r) = U_0 \left[ \left( 1 - e^{-a(r-r_0)} \right)^2 - 1 \right]$ where $U_0$ is the dissociation energy (in $\text{J}$), $r_0$ is the equilibrium interatomic distance (in $\text{m}$), $a$ is a positive constant (in $\text{m}^{-1}$), and $r$ is the distance between adjacent atoms (in $\text{m}$). Assuming the crystal fractures when the applied tensile force per atomic chain exceeds the maximum possible interatomic attractive force, what is the theoretical macroscopic breaking stress $\sigma_b$ (in $\text{N/m}^2$) of the material? (Assume the cross-sectional area per atomic chain remains $r_0^2$ up to the fracture point).