An element A crystallises in fcc structure. 200 g of this element has `4.12xx10^(24)` atoms. If the density of A is `7.2"g cm"^(-3)`, calculate the edge length of the unit cell.

Explanation

Let length of each edge = a cm
Volume of unit cell = `a^3 cm^3`
Density = `7.2 g cm^(-3)`
Mass of each atom = `(200)/(4.12 xx 10^(24))`
`= 48.54 xx 10^(-24) g`
No. of atoms per unit cell = 4(fcc)
Mass of unit cell = `4 xx 48.54 xx 10^(-24)`
`= 194.16 xx 10^(-24) g`
Now, density = `("Mass")/("Volume")`
`7.2 = (194.16 xx 10^(-24))/(a^3)`
or `" " a^3 = (194.16 xx 10^(-24))/(7.2) = 26.97 xx 10^(-24) cm^(3)`
or `" " a = 2.999 xx 10^(-8) cm = 299.9 p m`.