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How many atoms per square millimeter are there on (010) plane of lead? Assume the interatomic distance to be 3.499×10-10 m.

(a)  2.04 × 1012 atoms/mm2 

 (b)  8.16×1012 atoms/mm

(c) 16.32 × 1012 atoms/mm

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Correct option (b) 8.16 × 1012 atoms/mm2

Explanation:

Lead has FCC structure

The given interatomic distance = 3.499 × 10-10 m

∴ 2r = 3.499 × 10-10 m

If ‘a’ is the side of the square

∴√2a2 = 4r

∴ a = 4.95 × 10-10 m

Now, area of (010) plane = a2 = (4.95 × 10-10) 2 m2 

For FCC, Number of atoms in (010) plane = 2

∴ number of atoms per millimeter square

= 2/(4.95 x 10-10)2m2

= 8.16 × 1012 atoms/mm2

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