Question

Gold contacts are popular in electronic circuit boards owing to the fact that gold does not oxidize or corrode. However pure gold is very soft, so to harden it, it is sometimes alloyed with copper.

The resistivity of the alloy can be approximated by the Nordheim Mixing Rule:

$\rho$ _Alloy = $\rho$ _Au + C_N*x*(1-x)

Here, C_N is the Nordheim constant (450 nOhm-meters for Cu dissolved in Au) and x is the atomic fraction of Cu in the alloy Au1-x Cux alloy. (x<0.50) For the resistivity of gold, assume a value of 24.4 nOhm-meters.

A rectangular gold/copper contact is 5 mm long, 10 microns thick, and 2 mm wide and needs to have a resistance of 20 mOhms. What is the atomic fraction of copper that we need in the alloy ?

Answer 1

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