Many metals pack in cubic unit cells. The density of a metal and length of the unit cell can be used to determine the type for packing. For example, polonium has a density of 9.19 g/cm3 and a unit cell side length a of 3.37 Å. (1 Å = 1 10-8 cm.) (a) How many polonium atoms are in exactly 1 cm3? atoms (b) How many unit cells are in exactly 1 cm3? unit cells (c) How many polonium atoms are there per unit cell?

2.64 x 10²² polonium atoms are in exactly 1 cm³, 2.61 x 1022 unit cells are in exactly 1cm³ and one polonium atom is present in one unit cell.

What is cubic unit cells?

Unit cell is the simplest repeating structure of any body, so as the name suggested cubic unit cells are the repeating units of cubic structure.

In the question, given that:

Density of polonium = 9.19 g/cm³

Length of unit cell = 3.37 Å or 3.37 × 10⁻⁸ cm

(a). To calculate the no. of polonium atoms in 1 cm³, first we have to determine the average mass of one atom and that will be calculated as follow:
210g per mol ÷ 6.022 x 1023 atoms per mol = 34.866 x 10¯²³ g/atom

Now, we will divide the given mass to the average mass of one atom:

9.19g / 34.866x 10¯²³ g/atom = 2.64 x 10²² atoms in 1 cm³.

(b). To determine the no. of unit cells are in exactly 1 cm³ unit cells, calculation is as follow:
1 cm³ / (3.37 × 10⁻⁸ cm)³ = 2.61 x 1022 unit cells

(c). No. of polonium atoms in per unit cell is calculated as follow:

2.64 x 10²² atoms / 2.61 x 10²² unit cells = 1 atom per unit cell

Hence, polonium atoms are in exactly 1 cm³ is 2.64 x 10²², 2.61 x 1022 unit cells are in exactly 1cm³ and one polonium atom is present in one unit cell.

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