What is the radius of a metal atom if it crystallizes with body-centered lattice having a unit cell edge of 333 Pico meter?

1538.06 pm

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769.03 pm

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288.38 pm

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144.19 pm

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Solution

The correct option is D 144.19 pm
Given, a=333 pm
For body-centered unit cells, the relation between radius of a particle ‘r’ and edge length of unit cell ‘a’ is given as $\sqrt{3} a = 4 r$
On substituting the values we get $\sqrt{3} \times 333 = 4 r r = 144.19 p m$ .
Hence radius of the metal atom is 144.19 pm

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