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What do you mean by allotropy?

Answer
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Hint: In periodic table, allotropes are mainly present in the $13$ to $16$ group.
Different arrangements of the same element will result in different chemical and physical properties.
Allotropes consist of only one type of atom.

Complete step by step answer:
Allotropy is defined as the property of an element to present two or more forms. In this, atoms of an element are arranged in different manner. The phase remains the same but the arrangement differs. For example, oxygen has allotropes that means it can exist in dioxygen as well as ozone in solid, liquid and gas form.
There are three allotropes of carbon:
lets us discuss the three allotropes of carbon:
1.Diamond
It contains giant molecules of carbon atoms. Diamonds are lustrous because they reflect light and sparkle. It is used for cutting tools because it is very hard and has a high melting point. Diamonds do not conduct electricity and they are soluble in water. In diamond, every atom is bonded with its neighbour by four strong covalent bonds and hence they have no free electrons and ions. This is why diamonds do not conduct electricity.
2.Graphite
It has layers of carbon atoms. It is insoluble in water and is a good conductor of electricity. Hence, it is used in electrodes for electrolysis. Each carbon atom is bonded with three covalent bonds and hence they have one electron. That is why graphite is a good conductor of electricity.
3.Fullerene
In this we can see, the carbon atoms are bonded by single and double bonds and form a fused ring. The most famous member of fullerene is Buckminsterfullerene $({{C}_{60}})$ .

Note: Carbon atoms have many allotropes because it shows a wide range of physical properties.
Phosphorus atoms contain white and red allotropes.
Oxygen atoms contain dioxygen and ozone.
Sulphur atom contains cyclohexa sulphur (Cyclo $-{{S}_{6}}$ ), cyclohepta sulphur (Cyclo $-{{S}_{7}}$ ) and cyclo-octasulphur (Cyclo $-{{S}_{8}}$ )