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Question

A solid has a bcc structure. If the distance of closest approach between the two atoms is 1.73oA. The edge length of the cell is:

A
199pm
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B
3/2 pm
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C
142.2pm
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D
2pm
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Solution

The correct option is A 199pm

In bcc structure, the atoms are present at corners and at body center and the atoms along the body diagonal are touching each other.

So, if a is the edge length of the cube and r is the radius of the atom.

Then, 3a=4r

2r=3a2

Now, distance of closest approach is reached when two atoms are touching each other i.e their centers are at 2r distance from each other.

So, 32a=1.73 ˚A

a=1.73×23˚A=1.99 ˚A=199pm

Option A is correct.


1000646_936734_ans_a4b4e63fb1304a6a909c0e422d1bf36a.PNG

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