Answer
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Hint: In a molecule, a chiral center is an atom that is bonded to four different atoms or groups of atoms in such a manner that the atom has a non-superimposable mirror image. If an atom is not bonded to four non-identical atoms or groups of atoms and has a superimposable mirror image is known as an achiral center.
Complete step by step answer:
For an atom to be a chiral center it needs to have four non-identical atoms or groups of atoms.
In the case of a carbocation, only three bonds are possible due to a positive charge and therefore you will not get a non-superimposable mirror image and is not a chiral center.
When we consider a carbon radical, it will also form three bonds due to the presence of an unpaired electron instead of four and thus will have a superimposable mirror image rather than non-superimposable and therefore is not a chiral center.
In the case of ${{s}}{{{p}}^{{2}}}$ - hybridized carbon atom, there will be two single bonds and one double bond, thus a total of three bonds and therefore it is also not a chiral center but an achiral one.
In the case of ${{s}}{{{p}}^{{3}}}$ - hybridized carbon atom, there will be four bonds and in case, it has four different atoms or groups of atoms attached to it, it will form a non-superimposable mirror image and thus will be a chiral center.
Hence the correct answer is option D.
Note:
Chirality (the presence of more than one chiral center in a molecule) in a very important concept of stereochemistry and biochemistry. The stereochemistry of a molecule changes its property very much, for instance, one stereoisomer will be biologically active while the other will be not. Cisplatin is one such drug that has a therapeutic effect in its cis form but inactive in trans-form.
Complete step by step answer:
For an atom to be a chiral center it needs to have four non-identical atoms or groups of atoms.
In the case of a carbocation, only three bonds are possible due to a positive charge and therefore you will not get a non-superimposable mirror image and is not a chiral center.
When we consider a carbon radical, it will also form three bonds due to the presence of an unpaired electron instead of four and thus will have a superimposable mirror image rather than non-superimposable and therefore is not a chiral center.
In the case of ${{s}}{{{p}}^{{2}}}$ - hybridized carbon atom, there will be two single bonds and one double bond, thus a total of three bonds and therefore it is also not a chiral center but an achiral one.
In the case of ${{s}}{{{p}}^{{3}}}$ - hybridized carbon atom, there will be four bonds and in case, it has four different atoms or groups of atoms attached to it, it will form a non-superimposable mirror image and thus will be a chiral center.
Hence the correct answer is option D.
Note:
Chirality (the presence of more than one chiral center in a molecule) in a very important concept of stereochemistry and biochemistry. The stereochemistry of a molecule changes its property very much, for instance, one stereoisomer will be biologically active while the other will be not. Cisplatin is one such drug that has a therapeutic effect in its cis form but inactive in trans-form.
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