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In a cubic structure of diamond which is made from $X$ and $Y$ , where $X$ atoms are at the corners of the cube and $Y$ at the face centres of the cube . The molecular formula of the compound is :A: ${X_2}Y$B: ${X_3}Y$C: $X{Y_2}$D: $X{Y_3}$

Last updated date: 25th Jun 2024
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Hint:Whenever we are given a solid cube of a molecule , the positions of the substituent atoms determine the molecular formula of the compound. If the atom is in the edge centre it contributes $\dfrac{1}{4}$ to the particular molecule , if it is in the face centre it contributes $\dfrac{1}{2}$ to the molecule and if it is in the corner of the cube it contributes $\dfrac{1}{8}$ to the molecule.

In the given question it is given that the $X$ atoms are in the corners and the $Y$ atoms are in the face centre. In a given cube there are eight corners and six faces. So there will be eight $X$ atoms in the eight corners of the cube and six $Y$ atoms in the six faces of the cube. The contribution of the corner atoms to a cube is $\dfrac{1}{8}$ to the compound and the contribution of the face centred atoms to the compound is $\dfrac{1}{2}$ . So the molecular formula of the compound will be
${X_{\dfrac{1}{8}}}_{ \times 8}{Y_{\dfrac{1}{2}}}_{ \times 6} = X{Y_3}$
So from a the above explanation and calculation it is clear that the correct answer of the question is
D: $X{Y_3}$

Additional information : When a cube has eight atoms in eight corners and one atom in the body centre it is known as body centred cube. When a cube has eight atoms in eight corners and six atoms in the six faces of the cube it is known as a face centred cube.

Note: Always remember that the atoms in the corner constitute $\dfrac{1}{8}$ the compound , atoms in faces contributes $\dfrac{1}{2}$ ,atoms in the edge centre contributes $\dfrac{1}{4}$ and atoms in body centre contributes 1 to the compound. To find the molecular formula of the compound multiply the number of atoms in the particular positions with their respective contribution to the compound.