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Both red and white phosphorus are two physical forms of the same element phosphorus.
Diamond and graphite are both allotropes of carbon hence diamond and graphite are all made from the same element. The existence of isotopes does not explain the difference in properties between diamond and graphite because they are not isotopes of each other.
The difference between diamond and graphite lies in the arrangement of carbon atoms in the two structures. The carbon atoms are closely packed in diamond while they are sparsely packed in graphite.
An allotrope is a phenomenon which describes the existence of an element in different physical forms.
The fact that red phosphorus is fairly stable at room temperature in air, but white phosphorus can ignite easily when exposed to air is due to the existence of different allotropes. Both red and white phosphorus are two different physical forms of the same element phosphorus.
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