The compound which shows metamerism is:

Options

A. `C_3H_6O`
B. `C_4H_(10)O`
C. `C_5H_(12)`
D. `C_3H_8O`

Answer

To determine which compound shows metamerism, we first need to understand what metamerism is. Metamerism is a type of isomerism that occurs when two or more compounds have the same molecular formula but differ in the arrangement of alkyl groups around a functional group. This typically occurs in compounds like ketones, ethers, and secondary or tertiary amines.

### Step-by-Step Solution:

1. **Understanding Metamerism**:
- Metamerism occurs when there are different alkyl groups on either side of a functional group in a molecule.
- For example, in ethers, if we have R-O-R', the R and R' can be different alkyl groups.

2. **Analyzing the Given Options**:
- We will evaluate each option to see if it can exhibit metamerism.

3. **Option 1: C3H6O**:
- Possible structures:
- As an aldehyde: CH3-CH2-CHO (not metameric as CHO is fixed at one end).
- As a ketone: CH3-C(=O)-CH3 (not metameric as both sides are the same).
- Conclusion: **Does not show metamerism**.

4. **Option 2: C4H10O**:
- Possible structures:
- As an aldehyde: CH3-CH2-CH2-CHO (not metameric).
- As a ketone: CH3-C(=O)-CH2-CH3 (not metameric).
- As an ether: CH3-CH2-O-CH2-CH3 (can have variations like CH3-CH2-O-CH3).
- Conclusion: **Shows metamerism due to different alkyl groups**.

5. **Option 3: C3H8O**:
- Possible structures:
- As an aldehyde: CH3-CH2-CHO (not metameric).
- As a ketone: CH3-C(=O)-CH3 (not metameric).
- As an ether: CH3-O-CH2-CH3 (not metameric).
- Conclusion: **Does not show metamerism**.

6. **Final Conclusion**:
- The only compound that shows metamerism is **Option 2: C4H10O**.