Calculate the fraction of empty space in cubic closest packing to five significant figures.

0.259 52 . The fraction of empty space in a ccp cell is 0.259 52

Cubic closest packing is another name for face centred cubic.

Refer to the attached diagram of an fcc unit cell from hemantmore.

a.Number of atoms in unit cell

In an fcc lattice, there are eight atoms at the eight corners of the cube and one at the centre of each face

∴ No. of atoms

= 8 corners x (1/8 atom)/(1 corner) + 6 faces x (½ atom/1 face)

= 1 atom + 3 atoms = 4 atoms

b.Volume of atoms

Let r be the radius of an atom. Then

Volume of 1 atom = (4/3)πr^3

Total volume of atoms = 4 atoms × [(4/3)πr^3]/(1 atom) = (16/3)πr^3

The length of the diagonal AB is

AB = 4r

Let a be the edge length of the cube.

AB^2 = AC^^2 + BC^2

(4r)^2 = a^2 + a^2

16r^2= 2a^2

a^2 = 8r^2

a = rx8^½

V = a^3 = (rx8^½)^3 = 8r^3x8^½

PE = Volume of atoms/Volume of cell = [(16/3)πr^3]/[ 8r^3x8^½]

= 2π/(3x8^½)

Fraction of empty space = 1 - PE = 1 - 2π/(3x8^½) = 1 – 0.740 480

= 0.259 52

- "the choice that is not an indicator of a chemical change is "state of matter changes". more common than not, chemical reactions produce energy in the form of light or heat. along with energy, they also produce a new substance called the product that could be in any state of matter (solid, gas, or liquid)."

because of all the things that happen around the us, many people get into arguments which sadly could get physical, but we should actually make a change for that.