Stereospecificity of carbene addition

Problem 9.29 (a) Use the following observations to discuss stereospecificity of carbene addition, (b) Suggest mechanisms for addition of (i) singlet and (ii) triplet carbenes to alkenes. 

The stereospecificity of carbene additions has been widely used in experiments designed to determine the multiplicity of a carbene generated under given conditions. Stereospecific addition is taken as evidence for the involvement of the singlet species. The alternate result, formation of a mixture of the possible isomers, requires additional information for complete interpretation. Lack of stereospecificity implies some triplet carbene, but permits simultaneous involvement of the singlet species. 

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