Copper crystallises into a fcc structure and the unit cell has length of edge `3.61 xx 10^(-8)` cm. Calculate the density of the copper Atomic mass of copper is 63.5 g `mol^(-1)`

Answer

Density of Cu = 8. 97 g `cm^(-3)`

Explanation

Given : Crystalline structure of Cu is fcc
Edge length =a= `3.61 xx 10^(-8) cm`
Atomic mass of Cu= 63.5 g `mol^(-1)`
Avogadro number `=6.022 xx 10^(23) mol^(-1)` Density = d= ?
In fcc structure there are 8 Cu atoms at 8 corners and 6 Cu atoms at 6 face centres .
`:. ` Total number of Cu atoms `=(1)/(8) xx 8 + (1)/(2) xx 6 = 1 + 3 =4`
Mass of Cu atoms `=4 xx 1.054 xx 10^(-22)= 4.216 xx 10^(-22) g`
Mass of unit cell = Mass of 4 Cu atoms `= 4.216 xx 10^(-22) g`
Volume of unit cell =`a^(3) (3.61 xx 10^(-8))^(3) = 4.7 xx 10^(-23) cm^(3)`
Density of unit cell `= ("mass of unit cell" )/( "volume of unit cell" ) `
`:. d = (4.216 xx 10^(-23))/( 4.7 xx 10^(-23)) = 8.97 g cm^(-3)`