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  • A metal crystallises in bcc lattice. The % fraction of edge length not covered by atom is: Option: 1 <img alt="13.4\%" src="https://learn.career

A metal crystallises in bcc lattice. The % fraction of edge length not covered by atom is: 

Option: 1

13.4\%


Option: 2

16.2\%


Option: 3

12.6\%


Option: 4

10.5\%


Answers (1)

best_answer

We know: 

In \: \: bcc,\: \: r=\frac{\sqrt{3}a}{4}
 
Now, edge length of unit cell = 1 and radius of atom = r Therefore, edge length not covered by atom = a - 2r  
 
Thus, \: \: a\left [\frac{2-\sqrt{3}}{2} \right ]=a\left [\frac{2-\sqrt{3}}{2} \right ]\\\therefore \: \: percentage\: fraction\: not\: covered=\frac{a\frac{2-\sqrt{3}}{2}}{a}\times100=13.4\% 
 
Therefore, ?Option(1) is correct 

Posted by

Gautam harsolia

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