Question

How many atoms are in the following cubic unit cell -
(a) Simple cubic unit cell.
(b) Body centered cubic unit cell.
(c) Face centered cubic unit cell.​

Answer 1

SIMPLE CUBIC UNIT CELL:

8 contributions from each vertex of the cube;

Total number of atoms in a simple cubic unit cell is:

$\sf{ = 8 \times ( \dfrac{1}{8} th \: contribution)}$

$\sf{ = 8 \times \dfrac{1}{8} }$

$\sf{ = 1 \: atom }$

BODY CENTRED UNIT CELL:

Apart from 8 contributions from each vertex , there is an additional whole contributions from the body centre.

Hence , total number of atoms:

$\sf{ =( 8 \times \dfrac{1}{8}) + 1 }$

$\sf{ =1+ 1 }$

$\sf{ =2 \: atoms }$

FACE CENTRED UNIT CELL:

There are 8 contributions from each vertex and 6 contributions from each face of the cube:

$\sf{ =( 8 \times \dfrac{1}{8}) + (6 \times \dfrac{1}{2} )}$

$\sf{ =1+ 3}$

$\sf{ =4 \: atoms}$

Hope It Helps.

Answer 2

Answer:

atoms are in the following cubic unit cell -

(a) Simple cubic unit cell.

(b) Body centered cubic unit cell.

(c) Face centered cubic unit cell.​

(a) Simple cubic unit cell. =  in a simple unit cubic cell there are 8 corners and each have one atom so here we get ,

atoms in one unit cell = 8 ×1 /8 = 1 atom

(b) Body centered cubic unit cell. = body center cubic unit cell is belong from simple unit cell that is  

1 . 8 corner ×1/8 =1  atoms  per corner

2. 1 body centered atom = 1×1 =1  

total atom = 2

(c) Face centered cubic unit cell.​= in this unit cell we have atoms at all corner and one at face  in central position .

so,

8×1/8 =  1 atom

6 face centerd atom × 1/2 atom per unit  cell = 6 × 1/2 = 3 atoms

total atoms per cell = 4