E1 reaction question--> methide shift?

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Madnesor

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Hi, I have a question about the E1 reaction for 3- pentanol. When I tried to write out the mechanism, I included a 1,2 methide shift to stabilize the carbocation intermediate from a secondary--> tertiary carbocation. The answer does not include this step, thus the final product is different. Whey would no methide shift occur?
 
I don't follow?

The carbocation is formed on carbon 3, which is a secondary carbocation.

Is a C1->C2 shift even possible here? If you did a C2 -> C3 methyl shift, you would actually make a primary carbocation.

The H+ on C-2 simply gets removed and the electrons form a C2-C3 double bond.
 
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