An element having atomic mass 63.1 g/mol has face centered cubic unit cell with edge length `3.608 xx 10^(-8)` cm. Calculate the density of unit cell [Given `N_(A) = 6.022 xx 10^(23)` atoms/mol].

Explanation

(a)
`{:("In simple cubic unit cell , the number of particle is one i.e., considered as one sphere"),("The volume of one particle (1 sphere)" = 4/2 pir^(3)),("Radius of each particle (sphere)" = r):}}.....(i)`
The volume of the unit cell = `a^3 = (2r)^(3) = 8r^(3)`
`"Packing efficiency" = ("Volume occupied by 1 spheres")/("Total volume of the unit cell") xx 100`
Or `(Z xx "Volume of a particle")/("Volume of the unit cell") xx 100`
Packing efficiecy = `(4/3 pi r^3)/(8r^3) xx 100 = 52.4%`
(b) `d = (ZM)/(a^3 N_A)`
`d = (4 "atoms" xx 63.1 g//mol)/((3.608 xx 10^(-8) cm)^(3) xx (6.022 xx 10^(23)) "atoms/mol")`
`d = 8.92 g cm^(-3)`.