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

Let us assume z = 4 (fcc)
`d=(ZM)/(a^(3) xx Na)`
` 8.95 = (4 xx 63.54)/(a^(3) xx 6.02 xx 10^(23))`
`a^(3) = (254.16 xx 10^(-23))/(53.91)p 4.7145 xx 10^(-23)cm^(3)`
`a^(3) = 47.145 xx 10-24 cm^(3)`
` a = 3.612 xx 10 - 8 cm `
a = 361.2 pm
` 4r = sqrt(2a) ` (Fcc)
` r = (361.2)/(2 xx 1.414) = 127.7 ` pm
Cu has fcc structire.