In a solid having the Nacl structure.

Question

In  a solid state AB having Nacl structure,A atoms occupy the corners of the  cubic unit cell. If all the face centered atom along one of the axis  are axis are  removed the the resultant stoichiometry of the solid..                    a)AB2  b)A2B  c)A4B3 d) A3B4

Answer 1

According to NaCl structure  

so 'A' occupies 8 corners of the cubic unit cell which contribute 1/8 each to this cube  

 therefore 8*1/8 = 1   

also 6 face centered atoms contribute 1/2 to this cube   

therefore 6*1/2=3   

Therefore total contribution of atom'A' is 4   

Now B occupies octahedral voids(NaCl structure) which contribute 1/4  

 therefore 1+12*1/4 = 4   

So the formula is A4B4 or AB   

Now you are removing all the face centered atoms along one axis(any axis origin at centre of cube)   

so the number of atoms removed from cube are 2   

so contribution from 'A' remains 8*1/8(corner atoms) + 4*1/2(facecentered atoms) = 3   

so the resultant becomes A3B4

Comments

Thankyou sir.