What is the density of `Na_(2)O` having antifluorite-type crystgal stryctutre, if the edge length of cube is `100 gm` and what is the effect on density by `0.05%` Frenkel defect?

Options

A. `823.5 g cm^(-3)`, density decreases
B. `4.14.16 g cm^(-3)`, density decreases
C. `823.5 g cm^(-3)`, density remains same
D. `414.16 g cm^(-3)`, density remains same

Answer

D

Explanation

Density `(rho) = (Z_(eff) xx Mw)/(N_(A) xx a^(3))`
(For antifluorite, `Z_(eff) = 4//"unit cell"`)
`rho = (4 xx [23 xx 2 + 16])/(6 xx 10^(23) xx (100 "pm" xx 10^(-10)cm)^(3))`
`[{:(1 "pm" = 10^(-12)m),(=10^(-10)"cm"):}]`
`= 414 .16 g cm^(-3)`