`CH_3-CH_2-CH_3underset((1))overset(Br_2//hv)to(X)underset((2))overset(Mg//ether)to(Y)underset((3))overset(CH_3-Br)to`
`(Z)underset((4))overset(Cl_2//hv)to(W)underset((5))overset(CH_3OH)to(R)`
The product R is :

Options

A. `CH_3-oversetoverset(CH_3)(|)CH-CH_2-OCH_3`
B. `CH_3-CH_2-CH_2-CH_2-OH`
C. `CH_3-undersetunderset(OCH_3)(|)oversetoverset(CH_3)(|)C-CH_3`
D. `CH_3-undersetunderset(OH)(|)oversetoverset(CH_3)(|)C-CH_3`

Explanation

To solve the given question step by step, we will analyze each reaction in the sequence provided.

### Step 1: Bromination of Propane (CH₃-CH₂-CH₃)
- The first step involves the bromination of propane (CH₃-CH₂-CH₃) using Br₂ in the presence of light (hv).
- This reaction will lead to the formation of 2-bromopropane (X):

\[ \text{CH}_3-\text{CH}_2-\text{CH}_3 \xrightarrow{Br_2/hv} \text{CH}_3-\text{CH}(\text{Br})-\text{CH}_3 \]

### Step 2: Formation of Grignard Reagent (Y)
- In the second step, we treat 2-bromopropane with magnesium (Mg) in ether. This forms a Grignard reagent (Y):

\[ \text{CH}_3-\text{CH}(\text{Br})-\text{CH}_3 + \text{Mg} \xrightarrow{\text{ether}} \text{CH}_3-\text{CH}(\text{MgBr})-\text{CH}_3 \]

### Step 3: Reaction with Methyl Bromide (Z)
- The third step involves the reaction of the Grignard reagent (Y) with methyl bromide (CH₃Br). This will lead to the formation of tert-butyl bromide (Z):

\[ \text{CH}_3-\text{CH}(\text{MgBr})-\text{CH}_3 + \text{CH}_3\text{Br} \rightarrow \text{CH}_3-\text{C}(\text{Br})(\text{CH}_3)-\text{CH}_3 \]

### Step 4: Chlorination (W)
- In the fourth step, we perform chlorination of tert-butyl bromide (Z) using Cl₂ in the presence of light (hv). This can lead to the formation of two products, but the preferred product will be 2-chloro-2-methylpropane (W):

\[ \text{CH}_3-\text{C}(\text{Br})(\text{CH}_3)-\text{CH}_3 \xrightarrow{Cl_2/hv} \text{CH}_3-\text{C}(\text{Cl})(\text{CH}_3)-\text{CH}_3 \]

### Step 5: Reaction with Methanol (R)
- In the final step, we react 2-chloro-2-methylpropane (W) with methanol (CH₃OH). This will lead to the formation of an ether (R) through nucleophilic substitution:

\[ \text{CH}_3-\text{C}(\text{Cl})(\text{CH}_3)-\text{CH}_3 + \text{CH}_3\text{OH} \rightarrow \text{CH}_3-\text{C}(\text{OCH}_3)(\text{CH}_3)-\text{CH}_3 + \text{HCl} \]

### Final Product (R)
The final product R is:
\[ \text{R} = \text{CH}_3-\text{C}(\text{OCH}_3)(\text{CH}_3)-\text{CH}_3 \]