The density of copper metal is `8.95" g "cm^(-3)`. If the redius of copper atom be `127. 8` pm, is the copper unit cell simple cubic, body - centred or face- centred cubic ?
(Given : atomic mass of Cu = 63. 5 g/mol)

Explanation

If copper atom were simple cubic,
a =2 r=2 ` xx` 127.8 pm = 256. 6 pm
` Z = 1 : P = ( Z xx M)/( a^(3) xx N_(0)) = ( 1xx 63.54 " g mol"^(-1))/ (( 255.6 xx 10^(-10) "cm") ^(3) xx ( 6.02 xx 10^(23) mol^(-1)) ) = 6.34 " g cm" ^(-3)`
Actual ` p = 8.95 " g cm"^(-3)`
Hence, copper atom is not simple cubic.
If copper atom were body - centred.
` a = (4r)/(sqrt3) = ( 4xx 127.8)/(1.732) " pm" = 295.15` pm
` Z=2 , p = ( Z xx M)/( a^(3) xx N_(0)) = ( 2 xx 63.54 " g mol"^(-1))/ ( ( 295. 15 xx 10^(-10) "cm") xx 6.02 xx 10^(23) "mol" ^(-1)) = 8.21 " g cm"^(-3)`
Hence, copper atom is not body- centred.
If copper atom were face - centred.
`a= 2sqrt2r = 2xx 1.414 xx 127.8 "pm" = 361 . 4"pm"`
`Z=4 , p = ( Z xx M)/(a^(3)xxN_(0)) = ( 4xx63.54" g mol"^(-1))/((361.4xx10^(-10) "cm") xx 6.02 xx 10^(23) "mol" ^(-1))= 8.94 " g cm" ^(-3)`
Hence, copper is face - centred cubic.