Question

An element A and B constitutes bcc type crystalline structure. Element A occupies body center position and B is at the corners of a cube. What is the formula of the compound? What are the coordination numbers of A and B?

Answer 1

Hint: The formula for any compound can be determined using the voids that the atoms are forming in crystal lattice. We know that there are three main types of unit cell which when rotated in three dimensions forms the crystal lattice. As we know the question is saying about BCC so there will be eight atoms at all eight corners so take $\left( {\dfrac{1}{8}} \right){\,^{th}}$ part and solve further.

Complete step-by-step answer:
We have a unit cell which when rotated in all three dimensions it will form a complete crystal lattice. The unit cell is of three types mainly that are discussed, SCC BCC and FCC. In BCC (body centered crystal lattice) there are atoms at all eight corners like we have eight corners in a cube, then one atom just between the unit cell. You can imagine the crystal by taking eight corners of a cubic room and one in the middle of the room.
Now it was said in the question that element A occupies the body centered position and B is at the corner, so the effective number of atoms of A in the unit cell will be one.
Effective number of (A) atom in unit cell $ = 1$
Now, for element B we know that there are eight corner and each corner have $\left( {\dfrac{1}{8}} \right){\,^{th}}$ portion of atom then we can have,
Effective number of atom B= $\dfrac{1}{8} \times 8\, = \,1$
We get the ratio of both elements in a body centred cubic cell as $A:B = \,1:1$ hence the formula will be $AB$ .

Note: The determination of formula also depends upon the type of packing that the crystal was doing. If there is formation of CCP which is also called as “face centered crystal” which is having atoms on eight corners plus one at each face. Questions can also be solved using void information and coordination numbers. Coordination number is the nearest particle which is surrounding one atom.