Titanium metal has a density of `4.54 "g cm"^(-3)` and an edge length of 412.6 pm. In what cubic unit cell does titanium crystallise ?

Explanation

Density `d = (zM)/(a^(3)N_(0))`
`d = 4.54 g//cm^(3), M = 48 g mol^(-1), Z = ? N_(0) = 6.023 xx 10^(23) mol^(-1)`
If value of z is known, structure can be decided
`z = (d N_(0)a^(3))/(M) = (4.54 xx 6.023 xx 10^(23) xx (412.6 xx 10^(-10))^(3))/(48) = 4`
Thus, titanium has face-centred cubic structure