Q. 173.7( 31 Votes )

Which of the foll

Answer :

(i)



In a simple cubic lattice the atoms are located only at the corners of the cube.


Let us assume the edge length or the side of the cube = a


And the radius of each particle = r


The relation between radius and edge a


Can be given as a = 2r


The volume of the cubic unit cell = side3 = a3


= (2r3)


= 8r3


Number of atoms in unit cell


The volume of the occupied space


And we know that, the packing efficiency




= 52.36%


(ii)


Let us assume the edge length or the side of the cube = a


And the radius of each particle = r


The diagonal of a cube is always a


The relation between radius and the edge will be = 4r


Divide by root 3 we get A


Total number of atoms in body centred cubic


Number of atoms at the corner


Number of atoms at the centre = 1


Total number of atoms = 2


The volume of the cubic unit cell = side3


= a3


= (4r/a√3)3


The volume of the occupied space


Packing efficiency




= 68%


(iii) Let the base of the hexagon is a and the height is c


Each angle in hexagonal will be 60 degree at the base


Packing efficiency of


Hexagonal close- packed lattice



a = 2r c = 1.633a




= 74%


Thus, hexagonal close- packed lattice has the highest packing efficiency of 74%.


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