Step 1: Understanding the Topic:
This problem pertains to structural isomerism in organic chemistry. Isomers are compounds with the same molecular formula but different arrangements of atoms. Metamerism is a specific type of isomerism that occurs when different alkyl groups are attached to the same polyvalent functional group (such as $-O-$, $-S-$, $-NH-$, or $-CO-$). Essentially, the "distribution" of carbon atoms on either side of the functional group is shifted.
Step 2: Key Formulas and Approach:
To identify metamers:
Ensure the molecular formula is identical.
Identify a polyvalent functional group present in both.
Check if the nature of the alkyl groups on either side of the functional group has changed.
Step 3: Detailed Explanation:
Option (A): Propan-1-ol and Propan-2-ol. These are both alcohols ($C_3H_8O$) but differ in the position of the $-OH$ group on the chain. These are position isomers.
Option (B): $n$-butane and Isobutane. These are alkanes ($C_4H_{10}$) with different carbon skeletons. These are chain isomers.
Option (C): Propanone (ketone) and Propanal (aldehyde). They have the same formula ($C_3H_6O$) but different functional groups. These are functional isomers.
Option (D): Methyl propyl ether ($CH_3-O-C_3H_7$) and Diethyl ether ($C_2H_5-O-C_2H_5$). Both have the formula $C_4H_{10}O$.
In the first, the oxygen has a methyl ($C_1$) and a propyl ($C_3$) group.
In the second, the oxygen has two ethyl ($C_2$) groups.
Because the alkyl groups around the polyvalent oxygen are distributed differently, they are metamers.
Step 4: Final Answer:
The metamers are the ethers in option (D).