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Which of the following sets of compounds and ions have linear geometry?
(A)$C{H_4},NH_4^ + ,BH_4^ - $
(B)$CO_3^{2 - },NO_4^ - ,B{F_3}$
(C)$NO_2^ + ,C{O_2},N_3^ - $

Last updated date: 23rd Jul 2024
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Hint :The molecules in which atoms are in a straight line are called linear molecules. The shape of a compound or ion can be determined with the help of VSEPR theory (valence shell electron pair repulsion theory). We know that lone pairs repel each other. They are electrons with negative charge. Negative and negative repel each other, so the electrons which are unpaired try to get away from each other as much as possible.

Complete Step By Step Answer:
If we have a compound which has no lone pairs of electrons, it will form a linear compound. For example, consider the compound $Be{H_2}$ . It will form a linear compound because the hydrogens will repel each other as much as possible to make a straight line. Consider the compound$Be{F_2}$. There are lone pairs of electrons on fluorine atoms. But this compound is still linear because equal amounts of lone pairs repel each other so much to the farthest distance away that they can be from each other and will give a linear molecule. $NO_2^ + $ is $sp$hybridized and is linear and the bond angle is ${180^ \circ }$. $C{O_2}$ has two bond pairs and is linear. $N_3^ - $ is linear and has $sp$hybridization.
Therefore, option C is the correct answer.

Note :
The three-dimensional arrangement of atoms in a molecule is said to be molecular geometry. It included the shape of the molecule and also bond lengths, bond angles and other parameters that determine the position of each atom in the molecule.