Question

Calculate the density of Ca (s) in a face centered cubic unit cell. (The atomic radius of Ca is 1.97 Å)

Answer 1

1) Convert A^o to cm:

1.97 A^o x (1 cm/10⁸ A^o) = 1.97 x 10¯⁸cm

2) Calculate the volume of the unit cell:

(1.97 x 10¯⁸ cm)³ = 7.645 x 10¯²⁴ cm³

3) Calculate the average mass of one atom of Ca:

40.078 g mol¯¹ divided by 6.022 x 10²³ atoms mol¯¹ = 6.655 x 10¯²³ g

4) Calculate the mass of the 4 Calcium atoms in the face-centered cubic unit cell:

6.655 x 10¯²³ g times 4 = 2.66 x 10¯²² g

5) Calculate the density (value from step 4 divided by value from step 2):

2.66 x 10¯²² g / 7.645 x 10¯²⁴ cm³ = 34.79 g/cm³