Why white phosphorus is more reactive than red phosphorus?

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White phosphorus exists in p4 molecule. In the molecular strain is quite high and it tends to break it as early as possible.

On the other hand red phosphorus exists as polymer like structure.

In red phosphorus the molecules join to make long chains and that makes them chemically inert or less reactive.

For study of p4 molecule have a look at the link given below.

Why does phosphorus form P4 exists but P2 do not exists?

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