Assertion :Face centered cubic cell has $4$ atoms per unit cell. Reason: In $f c c$ unit cell, there are $8$ atoms at the corners and $6$ atoms at face centers.

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

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Assertion is correct but Reason is incorrect

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Both Assertion and Reason are incorrect

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Solution

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
In fcc unit cell, $8$ atoms are present at the corners and $6$ atoms are present at the face centres of the cube. So, the effective number of atoms $= \frac{1}{2} \times 8 + \frac{1}{2} + 6 = 1 + 3 = 4$

(Since the contribution of atom at the corner is $\frac{1}{8}$ and contribution of atom at face centre is $\frac{1}{2}$ per unit cell)
Thus, Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
Hence, the correct option is $A$

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Assertion :Face centered cubic cell has 4 atoms per unit cell. Reason: In fcc unit cell, there are 8 atoms at the corners and 6 atoms at face centers.

Assertion :Face centered cubic cell has $4$ atoms per unit cell. Reason: In $f c c$ unit cell, there are $8$ atoms at the corners and $6$ atoms at face centers.