install 10.9 on macbook A1181

Probably not, but it's impossible to be certain based on the information posted. Choose About this Mac from the Apple menu, click on More Info, and see if the model identifier is MacBook5,2; that model can run Mountain Lion and newer.

Note that Mavericks and Yosemite will only be available if you previously got them from the Mac App Store or the people at a physical Apple Store or elsewhere at Apple say so.

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All MacBooks from 2005-2010 have the same model number. Can you look on the bottom near the hinge and tell me the emc number?