An element with molar mass `2.7 xx 10^(-2) "kg mol"^(-1)` forms a cubic unit cell with edge length 405 pm. If its density is `2.7 xx 10^3 "kg m"^(-3)`, what is the nature of the cubic unit cell ? 

Explanation

Molar Mass (M) `= 2.7 xx 10^(-2) "kg mol"^(-1)`
Edge length of a unit cell = 405 pm
` = 4.05 xx 10^(-10) m`
Density of unit cell = `2.7 xx 10^3 "kg m"^(-3)`
Using formula `d = (Z xx M)/(a^3 xx N_A)`
we get ,
`Z = (2.7 xx 10^(3) xx 6.022 xx 10^(23) xx (4.05 xx 10^(-10))^3)/(2.7 xx 10^(-2))`
Z = 4.
Hence, unit cell is face-centred cubic.