Question

A crystalline form of copper has a density of 8.95 g/cm3 . If the radius of copper atoms is 127.8 pm, is the copper unit cell

A) simple cubic

B) Body-centered cubic

C) Face centered cubic

Please explain your answer

Answer 1

Density of crystal = 8.95 g/cm³

Radius of copper atom = 127.8 pm = 127.8*10^-10 cm

Mass of 1 Copper atom = 63.546 g/mol / 6.023*10²³

= 1.055x10^-22 grams

We know that for a simple cubic cell -

n = 1 and a = 2r

density, d = 1*1.055x10^-22 / 8*(127.8*10^-10)³

= 6.34 g/cm³ which is less than given density.

For body centered cubic cell,

n = 2 ans a = 4r/

density,d = 2*1.055x10^-22 / (4/)³*(127.8*10^-10)³

= 8.24 g/cm³  which is less than given density.

For a face centered cubic cell -

n = 4 and a = *r

density, d =  4*1.055x10^-22 / ()³*(127.8*10^-10)³

= 8.95 g/cm³ which is equal to the given density.

So, the copper unit cell is face centered cubic.