Please help with chem!

Question

What fraction of an atom does each contribute to the unit cell?

a. Simple cubic

b. Body centered cubic

c. Face centered cubic

Answer 1

Hi Ariel G.,

Weird question. I think what you mean is, how many atoms comprise a unit cell (taking sharing into account) for each of the packings.

Simple cubic: each corner shared 8 ways, eight corners/cell, 8/8-> 1 atom per cell

Face-centered cubic: each corner shared 8 ways, 8 corners/cell; each of 6 faces shared 2 ways each;8/8+6/2 -> 4 atoms/cell

body-centered cubic: each corner shared 8 ways, 8 corners; one unshared atom at center of each cell;8/8+1 --> 2 atoms/cell

-- Cheers, --Mr. d.

Answer 2

Similar to another problem you had asked

I think these pages have some nice images to help you visualize each.

https://msestudent.com/simple-cubic-unit-cell/

https://msestudent.com/body-centered-cubic-bcc-unit-cell/

https://msestudent.com/face-centered-cubic-fcc-unit-cell/

simple cubic unit cell ... has atoms at each of 8 corners of the cube

At a corner, what fraction of an atom is inside the cube?

Sum up the fraction from each of the 8 corners to determine the total number of atoms.

body-centered cubic unit cell ... has atoms at each of 8 corners and one right at the center of the cube

At a corner, what fraction of an atom is inside the cube?

Sum up the fraction from each of the 8 corners AND the whole one right at the center to determine the total number of atoms.

face-centered cubic unit cell ... has atoms at each of 8 corners and atoms on each of 6 faces of the cube

At a corner, what fraction of an atom is inside the cube?

On each face, what fraction of an atom is inside the cube?

Sum up the fraction from each of the 8 corners AND

sum up the fractions from each of the 6 faces to determine the total number of atoms.