What is the maximum number of layers of atom in close-packed planes that will lie within two imaginary parallel planes having a distance between them of `13sqrt((2)/(3))r` (where `r` is the radius of atom) in the copper crystal (fcc)?
(Consider the atoms to be within the parallel planes if their centres are on or within the two parallel planes).

Options

A. `5`
B. `6`
C. `7`
D. `8`

Answer

C

Explanation

Refer of Section 1.22[c(iv)].
Distance between two layer (`A` and `B`) `= c/2 = sqrt((8)/(3)) (r)`
`= sqrt((2)/(3))(2r)`
`[{:("Given distance between two imagniary"),("Plnae = 12(sqrt(2))/(sqrt(3))(r)):}]`
Let `K` is the number of imaginary planes.
Hence,
`K xx (sqrt(2))/(sqrt(3)).(2r) = 13(sqrt(2))/(sqrt(3))(r) rArr K = 13/12 = 6.5 approx 7`
Thus, maximum number of layers `= 7` (see figure below).