The lattice parameter of BCC lattice is "a". The plane density is defined as the number of atoms per unit area of the plane.
(i) The plane density of the (1 1 1) plane of the given BCC lattice is–
Text Solution
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(i)
Sol. The plane diagram of (1 1 1) plane in the BCC unit cell is
Area of plane = 
× 2 × a 2 = 
a 2
No. spheres on the plane = 
× 3 = 
∴ plane density = 
= 
(ii)
Sol. The plane diagram of (110) plane in the BCC unit cell is
Area of the plane = 
a 2 No. of spheres on the plane = 
× 4 + 1 = 2
∴ plane density = 
= 
(iii)
Sol. The plane diagram of (1 0 0) plane in the BCC unit cell is
Area of the plane = a
2 No. of spheres on the plane = 
× 4 =1
Plane density = 
(iv)
Sol. 
(r x + r)
2 = 
+ 
= 
+ 
= 
+ 
= 
or r x + r = 
or r x = 
– 
= 
(v)
Sol. 
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