In ceramic crystal systems Show that the Magnesium Oxide MgO

In ceramic crystal systems; Show that the Magnesium Oxide (MgO) has the sodium chloride (Rock-Salt) crystal structure, if rMq^+2 = 0 066 nm and r_o-2 = 0.132 nm Calculate the density of MgO, if the atomic masses are 24.312 and 16 g/mol for magnesium and oxygen, respectively?

Solution

Given data rc= r mg+2=.066nm, ra=r o-2=.132nm

First we need to calculate the ratio between cation and anion .so, that we can able to know whether which geometry it belongs to & what will be the coordination number rc/ ra= .066/.132=.5

Ratio of rc/ra=0.5 , the coordination number is 6 . the mgo has same ratio as well as coordination number as that of nacl . hence the given mgi has the same crystal structure of nacl .

(B): given data

Atomic mass of mg+2 = 24.312g/mol= Aa

Atomic mass of o-2= 16g/mol=Ac

We need to calculate density of mgo

Density=n×{Ac+Aa}/vc×Na

Vc = volume of unit cell =2×ra+2×rc=2×.66+2×.132=.396

Na= Avogadro number=6.023×10^23

Ac=24.312g/mol

Aa=16g/mol

n= 8×1/8+{6×1/2}=4

Density=4×(24.312+16)/.396×6.023×10^23=6.76×10^-22

Density = 6.76×10^-22×10^21=0.676g/cm^3