1.

(a) Calculate the packing efficiency in hexagonal close packing arrangement. (b) Mention one consequence of metal excess defect.

Answer»

Solution :(a)
Packing Efficiency in hcp arrangement.
In `Delta ABC" "AC^(2) = b^(2) = BC^(2) + AB^(2)`
`b^(2) = a^(2) + a^(2) = 2a^(2) or b = sqrt(2) a`
If r is the radius of the sphere, then b = 4r = `sqrt(2)` a
or `a = 2 sqrt(2)r`
Each UNIT cell in hcp has effectively 4 spheres. Total volume of four sphere is EQUAL to `4 xx ((4)/(3)) pi r^(3)` and volume of the cube is `a^(3) or (2 sqrt(2) r)^(3)`
Packing efficiency `= ("Volume OCCUPIED by four spheres in the unit cell" xx 100)/("Total volume of the unit cell")`
`= (4 xx (4)/(3) pi r^(3) xx 100)/((2 sqrt(2) r)^(3)) % = 74%`
(b) It imparts colour to the crystal.


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