How much volume of the simple cubic unit cell is empty space (i. e. not filled by the atoms)?

For simple cubic unit cell:

Let the edge length = a

Such that a = 2r  (where r is the radius of the atom)

Then radius of the atom =

Volume of the unit cell =

Number of atoms in simple cubic unit cell = 1.

Therefore, empty space = volume of cube - volume occupied by atom

Percentage of empty space =

Substituting the values:

Percentage of empty space =

Percentage of empty space =

Percentage of empty space = %.

Hence, % is the empty space of the simple cubic unit cell.

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