Step 1: Understanding Williamson's synthesis.
- Williamson’s synthesis involves the reaction of an alkoxide ion (\( R-O^- \)) with a primary alkyl halide (\( R'-X \)) via the SN2 mechanism.
- The reaction does not work well with tertiary alkyl halides due to steric hindrance, which favors elimination over substitution.
Step 2: Identifying the correct option.
- In di-tert-butyl ether (\( (CH_3)_3C-O-(CH_3)_3C \)), both alkyl groups are tertiary.
- The SN2 reaction fails for tertiary alkyl halides because they form carbocations, leading to elimination instead of substitution.
- Therefore, di-tert-butyl ether cannot be synthesized using Williamson’s synthesis.