Calculate the number of atoms per unit cell i | vedclass

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(C) In a face-centered cubic $(fcc)$ unit cell,atoms are present at all the corners and at the center of all the faces of the cube.$(i)$ Each atom at

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(C) In a face-centered cubic $(fcc)$ unit cell,atoms are present at all the corners and at the center of all the faces of the cube.$(i)$ Each atom at the corner is shared by $8$ adjacent unit cells,so the contribution of each corner atom to the unit cell is $\frac{1}{8}$. Since there are $8$ corners,the total contribution from corner atoms is $8 	imes \frac{1}{8} = 1$ atom.$(ii)$ Each atom at the face center is shared by $2$ adjacent unit cells,so the contribution of each face-centered atom to the unit cell is $\frac{1}{2}$. Since there are $6$ faces,the total contribution from face-centered atoms is $6 	imes \frac{1}{2} = 3$ atoms.Therefore,the total number of atoms per unit cell in an $(fcc)$ structure is $1 + 3 = 4$ atoms.

Calculate the number of atoms per unit cell in a face-centered cubic $(fcc)$ unit cell.

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