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A metal (atomic mass = 40) has a body ce...

A metal (atomic mass = 40) has a body centred cubic crystal structure. If the density of the metal is 4.50 g `cm^(-3)`, calculate the volume of the unit cell.

Text Solution

Verified by Experts

The correct Answer is:
`27.8xx10^(-24)`
`"Density of unit cell"=("Mass of unit cell")/("Volume of unit cell")`
`therefore"Volume of unit cell"=("Mass of unit cell")/("Density of unit cell")`
`"Mass of unit cell = Mass of each atom"xx" Mo. of atoms per unit cell"`
`=("Atomic mass")/("Avogadro's Number")xx"No. of atoms per unit cell"`
`=(("50 g mol"^(-1)))/((6.022xx10^(23)"mol"^(-1)))xx2=((100g))/(6.022xx10^(23))`
Density of unit cell `(rho)=5.96"g cm"^(-3)`
Volume of unit cell `=((100g))/(6.022xx10^(23)=(5.96"g cm"^(-3)))`
`=0.0278xx10^(-21)cm^(3)=27.8xx10^(-24)cm^(3)`
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