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Niobium crystallises in body centred cub...

Niobium crystallises in body centred cubic structure. If the atomic radius is 143.1 pm, calculate the density of the element. (Atomic mass = 93 u)

Text Solution

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Calculation of the edge of the unit cell.
For body centred cube (a) =`rxx(1)/(sqrt3)=(141.3"pm")xx(4)/(1.732)=330.4"pm"`
Calculation of the density of the unit cell
Density of unit cell `=(ZxxM)/(N_(0)xxa^(3))`
Edge length (a) =(330.4 pm)=330.4
Atomic mass (M) = 93 u = `"93 g mol"^(-1)`
No. of atoms in the unit cell (Z) = 2
Avogadro's number `(N_(0))=6.022xx10^(23)"mol^(-1)`
`"Density of unit cell"=(4xx("93 g mol"^(-1)))/((6.022xx10^(23)"mol"^(-1))xx(330.4)^(3)xx(10^(-30)"cm"^(3)))="8.58 g cm"^(-3)`
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