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Question

In the closest packing of spheres of uniform size, the ratio of radii of octahedral and tetrahedral holes is :


A

0.7320.414

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B

0.4140.155

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C

0.7320.225

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D

0.4140.225

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Solution

The correct option is D

0.4140.225


If you put a small ball there, it will be in contact with all four spheres. Thus,

bd = 2 (R + r). r = (2.45 R) / 2 - R
= 1.225 R - R
= 0.225 R

For tetrahedral void, rvoidrsphere0.225;

The octahedral hole is located at the centre of any four spheres that form a square. If we represent the radius of a ball fitting in the octahedral holes by r, and the radius of the sphere as R, then we have the relationship:


For Octahedral void, rvoidrsphere=0.414


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