NH4Br has a face-centered cubic unit cell in which the Br- anions occupy corners and face centers, while the cations fit into the hole between adjacent anions. What is the radius of Br- if the ionic radius of NH4 is 138.3 pm and the density of NH4Br is 2.429 g/cm3

Ionic radius of the bromide ion is 227.9 pm.

Explanation:

Number of atom in FCC unit cell = Z = 4

Density of ammonium bromide =

Edge length of cubic unit cell= a= ?

Molar mass of ammonium bromide = 98 g/mol

Formula used :  

where,

= density

Z = number of atom in unit cell

M = atomic mass

= Avogadro's number  

a = edge length of unit cell

On substituting all the given values , we will get the value of 'a'

Ionic radius of bromide ion = r

To calculate the edge length, we use the relation between the radius and edge length for FCC lattice:

Putting values in above equation, we get:

Ionic radius of the bromide ion is 227.9 pm.