Question

Does MgO have a structure like that of NaCl or ZnS? If the density of MgO is 3.58g/cm3, estimate the radius (in centimeters) of the O2â anions and of the Mg2+ cations.

Answer 1

The radius of O^2- is 1.5*10^-8 cm and the radius of

Mg ^2+ is 6.2*10^-9 cm

Step-by-step explanation:

Face centered cubic : 1/8 atoms on each edges + 1/2 atoms on each face

=
`(1)/(8)* 8 + (1)/(2)*6` = 4 effective atoms

MgO have a structure like NaCl forms a lattice of FCC.

density of the lattice =
`( z.M)/(a^3*Na)`

z : no of atoms

M: mass of the atoms

a: radius of the atom

Na: Avogadro's number

a^3(radius) =
`( 4*40.3)/(3.58*6.022*10^23)`

a^3 = 7.477 * 10^-23 cm^3

a = 4.21 * 10^-8 cm

Now calculating the anionic(ra O^2-) and cationic (rc Mg^2+)

in Fcc a = 2
`√(2) ra`

ra = 1.5*10^-8 cm

a = 2ra + 2rc

rc = a/2 -ra

rc = 6.2*10^-9 cm

The radius of O^2- is 1.5*10^-8 cm and the radius of Mg ^2+ is 6.2*10^-9 cm