Question

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?

Answer 1

Answer:

A.) 34.866 x 10¯23 g/atom

B.) 2.64 x 10^22 atoms in 1 cm3

C.) 1 atoms per unit cell

Explanation:

A) Calculate the average mass of one atom of polonium:

210g mol¯1 ÷ 6.022 x 1023 atoms mol¯1 = 34.866 x 10¯23 g/atom

B) Determine atoms in 1 cm3:

9.19g / 34.866x 10¯23 g/atom = 2.64 x 10^22 atoms in 1 cm3

Determine volume of the unit cell:

(3.37 x 10¯8 cm)3 = 3.827 x 10¯23 cm3

Determine number of unit cells in 1 cm3:

1 cm3 / 3.827 x 10¯23 cm3 = 2.61 x 1022 unit cells

C) Determine atoms per unit cell:

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