Question

cubic unit cell length of a side of the cubic UNIT CELL CUBICS MODE 1/8 of an atom remetallic radius of an atom Primitive Cubic The ma ching ang antage = ven Face-Centered Cubic (aka Cubic Close-Packed) The atoms are touching along a face diagonal 1/8 of an atom 1/2 of an atom of an atom Body-Centered Cubic The atoms are touching along a body diagonal. 1/8 of an atom whole atom

Answer 1

Answer 1. The first unit cell's name is Simple Cubic system or Primitive cubic system. It comprises of atoms only at the corners of the cube.

The second unit cell's name is Face-centred cubic system. It is so because, in this system, atoms occupy the corners of the cube as well as the face centres of each side of the cube.

The third unit cell's name is Body-centred cubic system due to the fact that it has atoms at the corners and 1 at the centre of the cube.

Answer 2. For primitive cubic system- a=2r, where a is the length of each side of the cube and r, the radius of the atom.

For face-centred cubic system- a=(2$\sqrt$2)r

For body centred cubic system, a$\sqrt$3=4r

Answer 3.

It shows 1/8th contribution because if we imagine the single cube in 3D arrangement, we can view it as kept in between 4 cubes and that corner atom is shared between these 4 cubes. Try to imagine it this way, look at the upper corner in the wall facing you in your room. Now place another cube above it, to its left and to its right.

1/2 contribution in face centred is due to the fact that the atom at the face's centre is shared between two cubes.

Answer 4. No of atoms associated is given by Z (no of atoms in unit cell)

for primitive cube, Z=1 (8* 1/8)

for face centred cube, Z=4 ( 8* 1/8 + 6* 1/2)

for body centred cube. Z=2 (1+ 8* 1/8)

Answer 5 Volume occupied by the unit cell is given by= Z* 4/3$\pi$r³