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The theory that can completely/properly explain the nature of bonding in [Ni(CO)4] is : 

(1) Werner's theory 

(2) Crystal field theory 

(3) Valence bond theory 

(4) Molecular orbital theory

2 Answers

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Answer is (4) Molecular orbital theory

In complex [Ni(CO)4] decrease in Ni–C bond length and increase in C–O bond length as well as it's magnetic property is explained by MOT.

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Answer is (4) Molecular orbital theory.

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