`X`-rays diffraction studies show that copper crystallizes in an fcc unit cell with cell edge of `3.608 xx 10^(-8) cm`. In a separte experiment, copper is determined to have a density of `8.92 g cm^(3)`. Calculate the atomic mass of copper.

Answer

`63.2 g mol^(-1)`

Explanation

If M is the molar mass of copper,
Density = `(Z xx M)/(a^3 xx N_A)`
`Z = 4` (for fcc)
Cell edge, `a = 3.61 xx 10^(-8) cm, N_A = 6.022 xx 10^(23)`
`8.92 = (4 xx M)/((3.61 xx 10^(-8))^(3) xx 6.022 xx 10^(23))`
or `M = (8.92 xx 6.022 xx 10^(23) xx (3.61 xx 10^(-8))^(3))/(4) = 63.2 g mol^(-1)`.