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Titanium metal has a density of 4.54 "g ...

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 ?

Text Solution

Verified by Experts

The correct Answer is:
fcc unit cell
Density `(rho)=(ZxxM)/(a^(3)xxN_(0)xx10^(-30))`
Density of unit cell `(rho) = 4.54"g mol"^(-3) or Z=(rhoxxa^(3)xxN_(0)xx10^(-30))/(M)`
Atomic mass of titanium (M) = 48 g `mol^(-1)`
Avogadro's no `(N_(0))=6.022xx10^(23)"mol"^(-1)`
Edge length of unit cell (a) = 412.6 pm = 412.6
`z=((4.54"g cm"^(-3))xx(412.6)^(3)xx(6.022xx10^(23)mol^(-1))xx(10^(-30)cm^(3)))/("48 g" mol^(-1))=4 ("fcc unit cell")`
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