The density of iron crystal is 8.54 gram `cm^(-3)`. If the edge length of unit cell is 2.8 Å and atomic mass is 56 gram `mol^(-1)`, find the number of atoms in the unit cell.
(Given : Avogadro's number `=6.022xx10^(23), 1Å = 1xx10^(-8)` cm)

Explanation

Given : Edge length of unit cell (a)
`=2.8 Å = 2.8xx10^(-8)cm`
Density `(rho)=8.54g cm^(-3)`
Molar mass (M) = 59 gm
Volume of unit cell `(a)^(3)`
`=(2.8xx10^(-8))^(3)`
`=21.95xx10^(-24)cm^(3)`
Number of atoms (Z) = ?
Formula, `rho = (Z xx M)/(a^(3)xx N_(A))`
`{:(," "Zxx56),(8.54=,bar(21.95xx10^(-24)xx6.022xx10^(23))),(" "Z=,ul(8.54xx21.95xx10^(-1)xx6.022)),(," "56):}`
`Z = 2.015 ~= 2`
Number of atoms in unit cell is 2.