(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

By considering the force-separation curve for two adjacent atoms in a solid, f(x), show that the Young’s modulus can be expressed on the microscopic scale as:

[tex]Y = - \frac{1}{x_0} \frac{df}{dx}\right| |_{x=x_0}[/tex]

(the | is meant to go allt he way form the top to bottom of df/dx)

where [tex]x_0[/tex] is the equilibrium seperation of the atoms

2. Relevant equations

[tex]f(x) = - \left(\frac{A}{x}\right)^7 + \left(\frac{B}{x}\right)^{13}[/tex]

(I'm assuming A and B should be 1 angstrom so 1E-10m)

3. The attempt at a solution

[tex]x_0[/tex] is found by doing f(x).dx = 0 to find where f(x) crosses the x axis.

[tex] E \equiv \frac{\mbox {tensile stress}}{\mbox {tensile strain}} = \frac{\sigma}{\varepsilon}= \frac{F/A_0}{\Delta L/L_0} = \frac{F L_0} {A_0 \Delta L} [/tex]

Y is the gradient of stress/straing graph

hmmmm

:(

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# Homework Help: Young's modulus in microscopic terms

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