Electrical engineers are evaluating the use of bronze (an alloy of copper and tin) for high-current bus bars in an industrial facility. The table lists the molar composition of two candidate bronzes and the concentration of delocalized conduction electrons per cubic centimeter, determined experimentally.
Alloy
Composition (mol % Sn)
Conduction electron concentration (×10²² electrons cm⁻³)
A
5
8.4
B
15
7.1
Pure Cu
0
8.5
Assume that electrical conductivity is directly proportional to the concentration of mobile electrons and that all other factors (temperature, crystal defects not due to tin, etc.) are identical.
(a) Using the proportional relationship provided, calculate the expected conductivity of Alloy A and Alloy B as a percentage of the conductivity of pure copper.
(b) The facility requires a minimum of 90 % of pure copper’s conductivity. Based on your calculation in part (a), which, if any, alloy meets this requirement?
(c) Explain, in terms of the "sea of electrons" model and the effect of tin atoms on the copper lattice, why increasing the tin content decreases the conductivity.