Multiple choice

In hcp (ABAB...) and ccp (ABCABC...) structure made up of sphere of equal size ,the volume occupied per sphere (including the empty space ) is (a= radius sphere):

  1. $5.66a^3$
  2. $1.33a^3$
  3. $2.66a^3$
  4. $7.40a^3$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In hcp/ccp, the packing efficiency is 74%. The volume of the unit cell is V_cell. The number of spheres per unit cell is 4. Volume of 4 spheres = 4 * (4/3) * pi * a^3 = 16/3 * pi * a^3. V_cell = (16/3 * pi * a^3) / 0.74 = 22.67 * a^3. The question asks for volume per sphere = V_cell / 4 = 5.66 * a^3.

AI explanation

In both hcp and ccp structures, there are 4 spheres per unit cell. The volume of a cubic unit cell is determined by its edge length a, where a = 4r/sqrt(2) for a ccp structure. The total volume of the cell is a^3, which equals 64*r^3/(2*sqrt(2)), approximately 22.62*r^3. Dividing this total volume by the 4 spheres gives the volume occupied per sphere as 5.66*r^3. The correct result is 5.66a^3.

Keep practicing — related questions