Best method for preparation of `CH_(3)-O underset(CH_(3))underset(|)overset(CH_(3))overset(|)(C)-CH_(3)` by williamson’s ether synthesis is

Options

A. `CH_(3)O^(Ө)+CH_(3)-underset(CH_(3))underset(|)overset(CH_(3))overset(|)(C)-Br`
B. `CH_(3)-underset(CH_(3))underset(|)(CH)-O^(Ө)+CH_(3)-underset(CH_(3))underset(|)(CH)-Br`
C. `CH_(3)-underset(CH_(3))underset(|)overset(CH_(3))overset(|)(C)-O^(Ө)+CH_(3)-Br`
D. `CH_(3)-underset(CH_(3))underset(|)overset(CH_(3))overset(|)(C)-OH+CH_(3)-Br`

Answer

To prepare the ether `CH3-O-CH(CH3)2` (tert-butyl methyl ether) using Williamson's Ether Synthesis, we need to follow these steps:

### Step-by-Step Solution:

1. **Identify the Reactants**:
- The ether we want to synthesize is `CH3-O-CH(CH3)2`.
- This indicates that we need a methyl group (`CH3`) and a tert-butyl group (`C(CH3)3`) for the ether synthesis.

2. **Choose the Alkyl Halide**:
- For the tert-butyl group, we will use tert-butyl bromide (`C(CH3)3Br`) as the alkyl halide.
- The methyl group will come from methyl iodide (`CH3I`), which is a good alkyl halide for this reaction.

3. **Select the Alkoxide**:
- The alkoxide we will use is derived from the alcohol corresponding to the methyl group.
- We can prepare the methyl alkoxide (`CH3O-`) by deprotonating methanol (`CH3OH`) with a strong base like sodium hydride (NaH) or sodium metal (Na).

4. **Perform the Nucleophilic Substitution**:
- In Williamson's Ether Synthesis, the alkoxide ion acts as a nucleophile and attacks the alkyl halide.
- The nucleophilic attack occurs via an SN2 mechanism, where the alkoxide (`CH3O-`) attacks the carbon atom bonded to the bromine in tert-butyl bromide (`C(CH3)3Br`), leading to the displacement of the bromine atom.

5. **Formation of the Ether**:
- The reaction will yield the desired ether:
\[ CH3O- + C(CH3)3Br \rightarrow CH3O-C(CH3)3 + Br^- \]
- The product formed is `CH3-O-CH(CH3)2`, which is tert-butyl methyl ether.

### Conclusion:
The best method for the preparation of `CH3-O-CH(CH3)2` by Williamson’s Ether Synthesis is to use methyl iodide as the alkyl halide and tert-butyl bromide as the alkyl halide, with methyl alkoxide as the nucleophile.