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What is the distance between two nearest...

What is the distance between two nearest neighbours in a bcc unit cell with an edge length of a?

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In a bcc unit cell, particles touch each other along the body diagonal. The length of this diagonal in terms of the radius ( r) of particle is 4r. Now, for a bcc unit cell, the relationship between r and a (edge-length) is: `r=sqrt3/4a`. The distance between two nearest neighbour in a bcc cell = `1/2xx` the length of body diagonal = `1/2xx4r=2r`
`=2xxsqrt3/4a=sqrt3/2a`.
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Knowledge Check

  • The edge length of body-centred cubic unit cell is asqrt3 . The distance between two nearest neighbours in this unit cell is-

    A
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  • Metallic potassium (atomi mass = 39) has a body centred crystal structure. In the unit cell of this crystal, the distance between two nearest neighbour is 4.52Å. The density of potassium (in kg*m^(-3) ) is-

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    B
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