Question

Apply Hume-Rothery Rules to Copper and Tin. Then, apply them to copper and silver.

Atomic Radius of Copper = 128 pm

Atomic Radius of Tin = 140 pm

Atomic Radius of Silver = 144 pm

Answer 1

Solution:

(Background)

Hume Rothery rules are set of rules that describe conditions under which an element can dissolve in a metal, thus forming a solid solution(alloy). The solid solutions can be either substitutuional solid solutions or interstitial solid solutions, each of them has different rules. These rules are based on size, electronegativity and crystal structure.

Substituional Solid solutions:

1. Size: the atoms should have same size. Size should not differ more than 15%
2. Electronegativity: The atoms must have approximately same electronegativity.
3. Crystal structure: The atoms must have same crystal structure.

Interstiatial solid solutions:

1. Size: The solute atoms must be smaller in size than solvent.
2. Electronegativity. Both must have similar electronegativity.

Applying Hume Rothery rules to Copper and Tin.

Atomic radius of Copper: 128pm,

Atomic radius of Tin: 140 pm.

Size: the diffrence in atomic radius is not more than 15%. . Henc size factor is okay.

Crystal structure: the crystal structure of Copper is face centered cubic and that of Tin is centered tetragonal.

Electronegativity: the electronegativity of Copper is 1.90 and that of Tin is 1.96. they are very close.

Since, copper and tin obey Hume Rothery rules, they will readily be miscible and form solid solution.

Applying Hume Rothery rules to Copper and Silver:

Atomic radius of Copper: 128pm

Atomic radius of Silver: 144pm

Size: the difference in atomic radius is not more than 15%. It is only 11%. therefore, size factor is okay.

Electronegativity: The elctronegativity of copper is 1.90 and that of Silver is 1.93. The elctronegativity is almost similar.

Crsytal structure: the cyrstal structure of both Copper and Silver is face centered cubic.

Since, Copper and silver obey Hume Rothery rules, they both will be miscible and form a solid solution.