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Density of a unit cell is the same as th...

Density of a unit cell is the same as the density of the substance. So, if the density of the substance is known, we can calculate the number of atoms or dimensions of the unit cell. The density of the unit cell is related to its formula mass (M), number of atoms per unit cell (z), edge length (a in cm), and Avogadro's constant `N_(A)`, as
`rho=(zxxM)/(a^(3)xxN_(A))`
Q. An element X crystallizes in a structure having an fcc unit cell of an edge 100 pm. if 24 g of the element contains `24xx10^(23)` atoms, the density is

A

2.40 g `cm^(-3)`

B

40 g `cm^(-3)`

C

4 g `cm^(-3)`

D

24 g `cm^(-3)`

Text Solution

Verified by Experts

The correct Answer is:
B
Given that `24xx10^(23)` atoms of the element has mass 24 g. So, `6.02xx10^(23)` atoms will have mass
`M=(24xx6.02xx10^(23))/(24xx10^(23))=6.02g`
The density is given by `rho=(zxxM)/(a^(3)xxN_(A))=(6xx6.02)/(100xx100xx100xx10^(-30)xx6.02xx10^(23))=40g" "cm^(-3)`
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