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Hint: We know that allotropes are different forms of the same element bonded together differently without changing the chemical representation. Allotrope of carbon only contains carbon elements bonded differently without any other element as impurity.
Complete step by step answer:
We know that carbon shows allotropism due to its catenation property and its ability to form \[p\pi - p\pi \] bond. It should be noted that carbon exists in three allotropic forms:
Crystalline form consists of diamond and graphite.
Amorphous form consists of coal and charcoal.
Fullerene consists of a Buckyballs form.
As carbon dioxide is not in the elemental state of carbon, it cannot form the allotrope of carbon.
So, the correct answer is Option D .
Additional Information:
In diamond, each carbon is joined to the other four carbon tetrahedrally and each carbon has \[s{p^3}\] hybridization. We know that diamonds do not have any free electrons. Hence, it is a bad conductor of electricity.
In graphite, each carbon is \[s{p^2}\] hybridized and has a layered structure. Here, each carbon has one free electron in p- orbital. So, it is a good conductor of electricity.
The chemical representation of fullerene is \[{{\text{C}}_{{\text{60}}}}\] and buckyballs are the most common type of fullerene which have football-like structure.
Note:
We know that carbon dioxide exists as a gas state and all the allotrope of carbon exists in solid-state. We can find the correct option by this method also.
Complete step by step answer:
We know that carbon shows allotropism due to its catenation property and its ability to form \[p\pi - p\pi \] bond. It should be noted that carbon exists in three allotropic forms:
Crystalline form consists of diamond and graphite.
Amorphous form consists of coal and charcoal.
Fullerene consists of a Buckyballs form.
As carbon dioxide is not in the elemental state of carbon, it cannot form the allotrope of carbon.
So, the correct answer is Option D .
Additional Information:
In diamond, each carbon is joined to the other four carbon tetrahedrally and each carbon has \[s{p^3}\] hybridization. We know that diamonds do not have any free electrons. Hence, it is a bad conductor of electricity.
In graphite, each carbon is \[s{p^2}\] hybridized and has a layered structure. Here, each carbon has one free electron in p- orbital. So, it is a good conductor of electricity.
The chemical representation of fullerene is \[{{\text{C}}_{{\text{60}}}}\] and buckyballs are the most common type of fullerene which have football-like structure.
Note:
We know that carbon dioxide exists as a gas state and all the allotrope of carbon exists in solid-state. We can find the correct option by this method also.
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