In bronze, copper forms fcc arrangement and tin occupies interstitial sites. The density of bronze sample is `7717 kg m^(-3)` and its lattice parameter is 3.903 Å. What is the approximate mole fraction of tin in the alloy?
(At. mass of Cu = 63.54u, Sn = 118.7u)

Options

A. 0.01
B. 0.04
C. `0.10`
D. 0.4

Answer

B

Explanation

In 1 mole of unit cells, there are 4 mol Cu atoms and x mol Sn atoms.
Volume of 1 mole unit cells = `(3.903xx10^(-8)cm)^(3)xxN_(A)=35.79cm^(3)`
Mass of 1 mole unit cells = `35.79cm^(3)xx"density"=276.2g`
Equalising the mass to number of Cu and Sn atoms
`4xx63.54+x xx118.7=276.2rArrx=0.1858`
Mole fraction of Sn = `(0.1858)/(4.1858)=0.0444`