Determine the number of atoms per unit cell in a (a) face-centered cubic, (b) body- centered cubic, and (c) diamond lattice.

a) 4 b) 2 c) 8

Explanation:

Each corner of the cube is shared by 8 different cells, therefore there is 1/8 of atom for each corner. Each face of the cube is shared by 2 different cells, therefore there is 1/2 of atom for each face. Finally, each atom inside the body is not shared by different cells.

a) For face-centered cubic we have 8 corner atoms and 6 face atoms:

b) For the body-centered cubic we have 8 corner atoms and 1 atom inside the body:

c) For diamond lattice we have 8 corner atoms, 6 face atoms and 4 atoms inside the body:

explanation: in any substance/object, the particles inside it (atoms/molecules) constantly move in random directions and with random speeds (this motion is called brownian motion). as a result, the particles have some kinetic energy (which is proportional to the temperature of the substance).

explanation:

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