What is the Atomic Force Constant in a Metal Bar Under Tension?

[R2Zero]

Homework Statement

Consider a metal bar of length L, cross-sectional area A, equilibrium atomic separation x, and Young's modulus E. When a tension force F is applied to the bar, it causes an extension ΔL. Calculate the atomic force constant k by deriving expressions for (a) the number of chains of atoms in any cross section, (b) the number of atoms in a single chain of length L, (c) the microscopic extension Δx between atoms, and (d) the tensile force f between atoms. (e) Write f= kΔx and show that k=Ex. (f) Calculate the value of k for a typical metal for which E = 1.2 GN/m$^{2}$ and x=0.16 nm.

Homework Equations

f=kΔx

k=Ex

stress = modulus x strain

F/A = E ΔL/L

ΔL= FL/(EA)

The Attempt at a Solution

Part f is probably the only part of the problem I feel confident about doing. As far parts a through e, I can't make heads or tails of how to derive the expressions involving atomic separation x. This problem seems to somewhat relate Hooke's law with elastic materials and a picture on my book describes the interatomic forces in the material as spring-like.

 

[afcartagenam]

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