which monosaccharide does not show optical isomerism:

Options

A. dihydroxy acetone
B. glyceraldehyde
C. erythrose
D. ribose

Answer

To determine which monosaccharide does not show optical isomerism, we need to analyze the options provided: dihydroxyacetone, glyceraldehyde, erythrose, and ribose.

### Step-by-Step Solution:

1. **Understand Optical Isomerism**:
- Optical isomerism occurs when a molecule can exist in two forms that are mirror images of each other (enantiomers). This usually happens in chiral molecules, which have at least one asymmetric carbon atom.

2. **Identify Asymmetric Carbon Atoms**:
- A carbon atom is considered asymmetric (or chiral) if it is attached to four different groups. The presence of such a carbon atom allows for the formation of enantiomers.

3. **Analyze Each Option**:
- **Dihydroxyacetone**: This molecule has the structure CH2(OH)C(=O)CH2(OH). It has no asymmetric carbon atom, making it achiral and thus it does not show optical isomerism.
- **Glyceraldehyde**: This molecule has one asymmetric carbon atom, making it chiral and capable of showing optical isomerism.
- **Erythrose**: This molecule has two asymmetric carbon atoms, making it chiral and capable of showing optical isomerism.
- **Ribose**: This molecule also has multiple asymmetric carbon atoms, making it chiral and capable of showing optical isomerism.

4. **Conclusion**:
- Since dihydroxyacetone is the only monosaccharide among the options that does not possess an asymmetric carbon atom, it does not show optical isomerism. Therefore, the correct answer is **dihydroxyacetone**.

### Final Answer:
**Dihydroxyacetone** is the monosaccharide that does not show optical isomerism.