Step 1: Understanding the Question:
The question displays an electrophilic addition reaction where bromine ($\text{Br}_2$) is added across the carbon-carbon double bond of a specific alkene. We must identify the final IUPAC name of the saturated dihalide product.
Step 2: Detailed Explanation:
Let's decode the skeletal structure of the reactant alkene shown in the image.
- There is a double bond.
- To the left of the double bond, the carbon is attached to two methyl groups (indicated by the fork shape). This is an isopropyl-like end.
- To the right of the double bond, the carbon is attached to a hydrogen (implied) and one methyl group.
- The full structure is: $\text{CH}_3 - \text{C}(\text{CH}_3) = \text{CH} - \text{CH}_3$.
Applying IUPAC nomenclature rules to the reactant:
1. The longest carbon chain containing the double bond has 4 carbons (butene).
2. Number from the left to give the substituent the lowest number.
The reactant is 2-methylbut-2-ene.
Now, perform the reaction: Addition of $\text{Br}_2$.
Electrophilic addition of halogens across a double bond is an anti-addition process. A bromine atom attaches to each of the two carbons that previously formed the double bond.
Reaction: $\text{CH}_3 - \text{C}(\text{CH}_3) = \text{CH} - \text{CH}_3 + \text{Br}_2 \rightarrow \text{CH}_3 - \text{C}(\text{Br})(\text{CH}_3) - \text{CH}(\text{Br}) - \text{CH}_3$.
Let's name this newly formed saturated product:
1. The longest carbon chain remains 4 carbons (butane).
2. Number from the left to give the substituents the lowest possible set of locants.
- At Carbon 2, there is a Methyl group and a Bromo group.
- At Carbon 3, there is a Bromo group.
3. List substituents alphabetically (Bromo before Methyl).
The IUPAC name is 2,3-dibromo-2-methylbutane.
Step 3: Final Answer:
The product is 2,3-dibromo-2-methylbutane, matching option (d).