Step 1: Understanding the Concept:
Carbohydrates are classified based on their functional groups and carbon chain length into aldoses and ketoses.
Many sugars are stereoisomers possessing multiple chiral carbons.
Diastereomers are stereoisomers that are not mirror images of each other.
Epimers represent a specific class of diastereomers that differ in their stereochemical configuration (the spatial arrangement of the hydroxyl group and hydrogen atom) at only one single asymmetric (chiral) carbon atom.
Step 2: Detailed Explanation:
Let us evaluate each pair of sugars to determine if they are epimers:
(A). D-glucose and D-mannose:
Both are six-carbon aldoses (aldohexoses) with the chemical formula \(\text{C}_6\text{H}_{12}\text{O}_6\).
When comparing their structures, they are identical at every carbon atom except for carbon-2 (C-2).
In D-glucose, the hydroxyl group on C-2 is on the right side, whereas in D-mannose, the hydroxyl group on C-2 is on the left side.
Therefore, D-glucose and D-mannose are C-2 epimers.
Thus, (A) is correct.
(B). D-Ribose and D-ribulose:
D-ribose is a five-carbon aldose (aldopentose), and D-ribulose is its corresponding five-carbon ketose (ketopentose).
They are functional isomers (aldose-ketose isomers), not epimers.
(C). D-galactose and D-glucose:
Both are aldohexoses with the same chemical formula.
When comparing their structures, they are identical at every carbon atom except for carbon-4 (C-4).
In D-glucose, the hydroxyl group on C-4 is on the right, while in D-galactose, it is on the left.
Therefore, D-glucose and D-galactose are C-4 epimers.
Thus, (C) is correct.
(D). D-glyceraldehyde and Dihydroxyacetone:
These are three-carbon sugars (trioses).
D-glyceraldehyde is an aldotriose, and dihydroxyacetone is a ketotriose (it does not even contain a chiral carbon).
Therefore, they are structural functional isomers, not epimers.
Hence, the correct pairs of epimers are (A) and (C), which corresponds to option (B).
Step 3: Final Answer:
Consequently, the correct option representing the pairs of epimers is (B).