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An element 'X' has bcc lattice as shown ...

An element 'X' has bcc lattice as shown below :
The unit cell length, a is 306 pm.
(a) What is the distance between nearest neighbours?
(b) What is the distance between next nearest neighbours?
(c) How many nearest neighbours does each X atom have ?
(d) How many next nearest neighbours does each X have ?

Text Solution

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(a) The body diagonal is `sqrt(3).a = 1.732 xx 306 = 530 ` pm
Nearest neighbours along body diagonal are half the body diagonal.
`:.` Distance between nearest neighbours = `530/2 = 265` pm
(b) The next nearest neighbours are along the edge.
`:.` Distance between next nearest neighbour = 306 pm
(c) 8, because the body centre is next to 8 corners.
(d) 6, becuase each corner has neighbours along each edge.
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