In CsBr, Br− ions are present at each corner and Cs+ ion is at body center. So, there is 1 formula unit of CsBr per unit cell.
Theoretical density of crystal, ρ=nMNoa3 g/cm3
So, n=1; M=132.9+79.9=212.8 g/mol; ρ=4.44 g/cm3
⇒a3=nMρ No
⇒a3=1×212.84.44×6.022×1023
⇒a=(79.6)1/3×(10−24)1/3 cm
⇒a=4.3×10−8 cm=430 pm
So, edge length of unit cell =430 pm
So, on the body diagonal, Cs+ ion at body center and Br− ion at the corner are touching each other. So, if r+ is radius of Cs+ and r− is radius of Br−. Then,
2(r++r−)=√3a
⇒r++r−=√32×430 pm
⇒r−=372.4−174=198.4 pm
Total volume of unit cell =a3=(4.3×10−8)3=79.6×10−24 cm3
Volume occupied, V= Volume occupied by Br− ions + Volume occupied by Cs+ ions.
V=43π(r3−+r3+)
V=43π((1.98)3+(1.74)3)×10−24 cm3
V=54.6×10−24 cm3
Fraction of volume occupied =54.6×10−2479.6×10−24=0.68