Question

Krypton crystallizes with a face-centered cubic unit cell of edge 559 pm. 

 i. What is the density of solid krypton? 

 ii. What is the atomic radius of krypton? 

 iii. What is the volume of one krypton atom? 

 iv. What percentage of the unit cell is empty space if each atom is treated as a hard sphere? 

Answer 1

Given: Edge length (a) 

= 559 pm = 5.59 x 10⁻⁸ cm 

 z = 4 (FCC) Atomic mass of Krypton (M) = 83.798 

To find: i. Density of solid krypton = ? 

 ii. Atomic radius of krypton =? 

 iii. Volume of one krypton atom = ? 

 iv. % of the unit cell which is empty space = ? 

Formula: 

Calculation: 

From formula (i),

Volume of the 4 atoms in the unit cell: