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Sodium crystallises in a cubic lattice a...

Sodium crystallises in a cubic lattice and the edge length of the unit cell is 430 pm. Calculate the number of atoms in the unit cell. (Atomic mass Na = 23 amu, Density of Na = 0.9623 g `cm^(-3)`)

Text Solution

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The correct Answer is:
2, bcc
`"Density"(rho)=(zxxM)/(a^(3)xxN_(0)xx10^(-30))or z=(rhoxxa^(3)xxN_(0)xx10^(-30))/(M)`
Edge length (a) = 430 pm = 430 , Atomic mass of Na (M) = 23 amu = 23 g `mol^(-1)`
Avogadro's No. `(N_(0))=6.022xx10^(23)"mol"^(-1)` , Density of Na `(rho)=0.9623"g cm"^(-3)`
`z=((0.9623"g cm"^(-3))xx(430)^(3)xx(6.022xx10^(23)mol^(-1))xx(10^(-30)cm^(3)))/(("23 g" mol^(-1)))=2 ("bcc structure").`
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