Step 1: Understanding the Concept:
Dehydrohalogenation (an E2 elimination reaction) removes a halogen atom and a hydrogen atom from an adjacent ($\beta$) carbon, creating a carbon-carbon double bond. The number of isomeric alkenes depends on the number of different types of $\beta$-hydrogens and the possibility of geometrical (cis/trans or E/Z) isomerism in the resulting alkenes.
Step 2: Detailed Explanation:
Let's analyze each option independently:
(a) 1-Bromo-2-methylbutane: $\text{Br-CH}_2\text{-CH(CH}_3\text{)-CH}_2\text{-CH}_3$
The halogen is at C1. The only adjacent carbon is C2.
Removal of H from C2 gives: $\text{CH}_2\text{=C(CH}_3\text{)-CH}_2\text{-CH}_3$ (2-methylbut-1-ene).
This terminal alkene does not exhibit geometrical isomerism. Total isomers = 1.
(b) 2-Bromopropane: $\text{CH}_3\text{-CH(Br)-CH}_3$
The $\beta$-carbons are identical (both are methyl groups).
Elimination gives: $\text{CH}_2\text{=CH-CH}_3$ (Propene).
Propene has no geometrical isomerism. Total isomers = 1.
(c) 2-Bromopentane: $\text{CH}_3\text{-CH(Br)-CH}_2\text{-CH}_2\text{-CH}_3$
There are two different adjacent carbons with hydrogens: C1 and C3.
Elimination with C1 gives: $\text{CH}_2\text{=CH-CH}_2\text{-CH}_2\text{-CH}_3$ (Pent-1-ene) $\rightarrow$ No geometrical isomerism (1 isomer).
Elimination with C3 gives: $\text{CH}_3\text{-CH=CH-CH}_2\text{-CH}_3$ (Pent-2-ene).
Pent-2-ene can exist as both {cis}- and {trans}- isomers (2 isomers).
Total isomers = 1 + 2 = 3.
(d) 2-Bromo-3,3-dimethylpentane: $\text{CH}_3\text{-CH(Br)-C(CH}_3\text{)}_2\text{-CH}_2\text{-CH}_3$
The $\beta$-carbons are C1 and C3. However, C3 is a quaternary carbon (it has no hydrogens attached to it!).
Therefore, elimination can only occur by removing a hydrogen from C1.
Product: $\text{CH}_2\text{=CH-C(CH}_3\text{)}_2\text{-CH}_2\text{-CH}_3$ (3,3-dimethylpent-1-ene).
No geometrical isomerism possible. Total isomers = 1.
Step 3: Final Answer:
2-Bromopentane gives the maximum number of isomeric alkenes (3 isomers).
Major products A and B formed in the following reaction sequence , are