The isomeric deuterated bromide with molecular formula C4H8DBr having two chiral carbon atoms is:

Step 1: Understand the requirement

Molecular formula: $\ce{C4H8DBr}$ (deuterated bromide)

Requirement: Two chiral carbon atoms

Step 2: Analyze each option

(a) 2-Bromo-1-deuterobutane:

Structure: $\ce{CH2D-CHBr-CH2-CH3}$

• C-1: $\ce{CH2D}$ - has 2 H atoms (not chiral)
• C-2: $\ce{-CH2D}$, $\ce{-H}$, $\ce{-Br}$, $\ce{-CH2CH3}$ (4 different groups) → chiral ✓
• C-3: $\ce{CH2}$ - has 2 H atoms (not chiral)
• C-4: $\ce{CH3}$ - has 3 H atoms (not chiral)

Total: 1 chiral center ✗

(b) 2-Bromo-2-deuterobutane:

Structure: $\ce{CH3-CDBr-CH2-CH3}$

• C-2: has Br, D, and two different alkyl groups
• But C-2 has: $\ce{-CH3}$, $\ce{-D}$, $\ce{-Br}$, $\ce{-CH2CH3}$ (4 different groups) → chiral ✓
• Other carbons: not chiral

Total: 1 chiral center ✗

(c) 2-Bromo-3-deuterobutane:

Structure: $\ce{CH3-CHBr-CHD-CH3}$

• C-2: $\ce{-CH3}$, $\ce{-H}$, $\ce{-Br}$, $\ce{-CHD-CH3}$ (4 different groups) → chiral ✓
• C-3: $\ce{-CHBr-CH3}$, $\ce{-H}$, $\ce{-D}$, $\ce{-CH3}$ (4 different groups) → chiral ✓

Total: 2 chiral centers ✓✓

(d) 2-Bromo-1-deutero-2-methylpropane:

Structure: $\ce{CH2D-CBr(CH3)-CH3}$

• C-2: has two $\ce{CH3}$ groups (not chiral)
• C-1: $\ce{CH2D}$ - has 2 H atoms (not chiral)

Total: 0 chiral centers ✗

Answer: (c) 2-Bromo-3-deuterobutane

Key Points:

• Deuterium (D) is an isotope of hydrogen (²H)
• D and H are different for chirality purposes
• A carbon with H and D (plus 2 other different groups) is chiral
• Chiral center: Carbon with 4 different groups
• For 2 chiral centers: $2^2 = 4$ stereoisomers (unless meso)