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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. A metal A (atomic mass=60) has a body-centred cubic crystal structure. the density of the metal is 4.2 g `cm^(-3)`. the volume of unit cell is

A

`8.2xx10^(-23)cm^(3)`

B

`4.74xx10^(-23)cm^(3)`

C

`3.86xx10^(-23)cm^(3)`

D

`5.86xx10^(-23)cm^(3)`

Text Solution

Verified by Experts

The correct Answer is:
B
The density is given by `rho=(zxxM)/(a^(3)xxN_(A))`. Therefore, `a^(3)=(2xx60)/(4.2xx6.02xx10^(23))=4.74xx10^(-23)cm^(3)`.
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