(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

:(

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Young's modulus in microscopic terms

**Physics Forums | Science Articles, Homework Help, Discussion**