Q 13 Niobium crystallises in body–centred cubic structure. If density is 8.55 g cm–3, alculate atomic radius of niobium using its atomic mass 93 u.

Q 13 Niobium crystallises in body–centred cubic structure. If density is 8.55 g cm^–3, alculate atomic radius of niobium using its atomic mass 93 u.

Edge of length of cell a = ?

Density p = 8.55 g /cm³

Number of atoms in unit cell of BCC lattice Z = 2

Avogadro number N_A = 6.022x10²³

Use formula

Density 

  

Cross multiply we get 

pa³N_A= ZM

Divide by PN_A we get

   

Plug the values we get 

        

Take cube root both side we get 
         

Plug the value of a we get