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b) Atoms of element B form hep lattice a...

b) Atoms of element B form hep lattice and those of element A occupies `2//3^(rd)` of tetrahedral voids. Calculate the formula of the compound formed by A and B. 

Text Solution

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The hcp lattice is formed by element `B`
First method
`:. Z_(eff)` of `B` (hcp lattice) `= 6`
Number of `TV = 8//"unit cell"`
Number of `OV = 4//"unit cell"`
Since elements `A` occupies two-thirds of `TV_(s)`
`:.` Number of `A = (2)/(3) xx 12 = 8`
`:.` Formula `= A_(8)B_(6) = A_(4)B_(3)`
Second method
Let `Z_(eff)` of `B = 1`
Number of `TV = 2//"atom"`
Number of `OV = 1//"atom"`
`:.` Number of `A = (2)/(3) xx TV = (2)/(3) xx 2 = (4)/(3)`
`:.` Formula `= A_(4//3)B_(1)`
Simplifying: `A_(4)B_(3)`
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