An element with density 2.8 g `cm^(-3)` forms a fcc unit cell with edge length `4 xx 10^(-8)` cm. Calculate the molar mass of the element. (Given : `N_(A) = 6.022 xx 10^(23) mol^(-1)`)

Explanation

d = 2.8 g `cm^(-3)`, z = 4 (for fcc), a = 4 `xx 10^(-8)` cm, `N_(A) = 6.022 xx 10^(23) mol^(-1)`
`d = (Z xx M)/(N_(A) xx a^(3))`
`M = (d xx a^(3) xx N_(A))/(Z)`
`= (2.8 g cm^(-3) (4 xx 10^(-8) cm)^(3) xx 6.022 xx 10^(23))/(4)`
`M = 2.8 xx 16 xx 20^(-1) xx 6.022`
= 26.97 g `mol^(-1)`