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The radius of a single atom of a generic element x is 161 pm and a crystal of x has a unit cell that is a simple cubic. Calculate the volume of the unit cell

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mahima6824soni

The volume of the unit cell that is a simple cubic is 1.1661622e⁻²⁰.

What is Volume?

Volume is the space occupied by a three-dimensional object.

By the formula of volume of atom

[tex]\rm Volume(atom) = \dfrac{4}{3} \times \pi \times r^3\\Volume(atom) = \dfrac{4}{3} \times \pi \times (161 \times 10^-^2^3)^3\\Volume(atom) = 2.1574e^-^2^1[/tex]

There are total 4 atoms, in a  FCC unit cell.

The total volume is

[tex]2.1574e-21 \times 4 = 8.6296e^-^2^1[/tex]

Volume of a unit cell will be

[tex]\dfrac{8.6296e-21}{0.74} = 1.1661622e^-^2^0[/tex]

Thus, the volume of the unit cell is [tex]\rm 1.1661622e^-^2^0[/tex]

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