Solid State - Result Question 13

####13. A metal crystallises in a face centred cubic structure. If the edge length of its unit cell is ’ $a$ ‘, the closest approach between two atoms in metallic crystal will be

(2017 Main)

(a) $2 a$

(b) $2 \sqrt{2} a$

(c) $\sqrt{2} a$

(d) $\frac{a}{\sqrt{2}}$

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Answer:

Correct Answer: 13. (d)

Solution:

  1. For fcc arrangement, $4 r=\sqrt{2} a$

where, $r=$ radius and $a=$ edge length

$\therefore$ Closest distance $=2 r=\frac{\sqrt{2} a}{2}=\frac{a}{\sqrt{2}}$



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