Which isomer of 1-bromo-4-tert-butylcyclohexane reacts faster when refluxed with potassium tert-butoxide?

See explanation.

Explanation:

Since potassium tert-butoxide is a strong bulky base, we expect that an elimination reaction predominates.

This reaction is expected to occur by E2 mechanism. The cis isomer of  1-bromo-4-tert-butylcyclohexane is known to react faster by E2 mechanism because it fulfills the anticoplanar arrangement required for for E2 mechanism, where the leaving group and adjacent proton must be anti to each other and in the same plane. The trans isomer can not fulfill this requirement.

14 days is the half-life of phosphorus-32