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Potassium crystallises in a bcc lattice ...

Potassium crystallises in a bcc lattice as shown in figure :
(a) What is the distance the nearest neighbours ?
(b) What is the distance between the next nearest neighbours ?
(c) How many nearest neighbours does each potassium atom have ?
(d) How many next nearest neighbours does each potassium atom have ?

Text Solution

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(a) The body diagonal is `=sqrt3a=sqrt3xx5.20Å=9.01Å`
The nearest neighbours along that diagonal are at half distance apart `=(9.01)/(2)=4.50Å`
(b) The distance between the next nearest neighbours `=5.20Å` along the cell edge.
(c) Nearest neighbours which surround each potassium atom = 8
(d) Since the C.N. of each potassium atom is six, the next nearest neighbours which surround each potassium atom = 6.
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