The density of an ionic compounds `(Mw = 58.5)` is `2.165 kg m^(-3)` and the edge length of unit cell is `562` pm, then the closest distance between `A^(o+)B^(ɵ)` and `Z_(eff)` of unit cell is

Options

A. `281` pm, `4`
B. `562` pm, `2`
C. `562` pm, `4`
D. `281` pm, `2`

Answer

A

Explanation

`rho=(Z_(eff)xxMw)/(a^(3) xx N_(A))`
`2.165 kg m^(-3) = (Z_(eff) xx 58.5 xx 10^(-3)kg mol^(-1))/((562 xx 10^(-12))^(3)m^(3) xx 6 xx 10^(23)"atoms")`
`:. Z_(eff) = 4` (fcc-type structure).
For `fcc`,
`d_(A^(o+))-B^(ɵ) = (a)/(2) = (562)/(2) = 281 "pm"`