Question

A solid has a structure in which W atoms are located at the corners of a cubic lattice, O atoms at the centre of the edges and Na atoms at the centre of the cubic. The formula for the compound is:
(A) $NaW{{O}_{2}}$
(B) $NaW{{O}_{3}}$
(C) $N{{a}_{2}}W{{O}_{3}}$
(D) $NaW{{O}_{4}}$

Answer 1

Any crystal lattice is made up of a very large number of unit cells which generate the entire lattice in different repeated directions and every lattice point is occupied by one constituent particle-like atom or molecule or ion. Assume that the constituent particle is an atom, there are three types of cubic units cells.

Complete step by step solution:
There are three types of cubic unit cells
(1) Primitive Cubic Unit Cell
(2) Body Centred Cubic Unit Cell
(3) Face Centred Cubic Unit Cell
Given, in a unit cell, W atoms are at eight corners of the cube. An atom contributes one eight to the unit cell in each corner.
The contribution of W atoms to the unit cell = $\dfrac{1}{8}X8=1$
O atoms at the centre of 12 edges. Each edge centre atom contributes one fourth to the unit cell.
The contribution of O atoms to the unit cell = $\dfrac{1}{4}X12=3$
The atom at the centre of the cube is Na. In body centre atoms contribute one to the unit cell.
The contribution of Na to the unit cell = 1
The ratio of atoms in cube W: O: Na = 1:3:1
Hence, the formula for the compound = $NaW{{O}_{3}}$

The correct answer is option B.

Note: A unit cell is the small portion of a crystal lattice. It is characterized by its dimensions along the three-edged, a, b, and c, which may or may not be mutually perpendicular. Three edges and the angles between the edges are the six parameters characterized by a unit cell.