To determine which of the given molecules will not show optical activity, we need to identify achiral compounds. Optical activity is a property of chiral molecules, which have non-superimposable mirror images. Achiral molecules, on the other hand, have a plane of symmetry and do not exhibit optical activity.
### Step-by-Step Solution:
1. **Understand Optical Activity**:
- Optical activity is exhibited by chiral molecules that lack a plane of symmetry. Chiral centers typically have four different substituents attached to them.
2. **Identify Chiral Centers**:
- Examine each molecule to identify any chiral centers. A carbon atom is considered chiral if it is bonded to four different groups.
3. **Analyze Each Structure**:
- For the first structure, if we have a carbon with groups COOH, H, OH, and another COOH, it has four different substituents. Thus, it is chiral and will show optical activity.
- For the second structure, if we have a carbon with groups H3C, CH, CD, and OH, again, it has four different substituents, making it chiral and optically active.
- For the third structure, if we have CH3, H, OH, H, and CH3, we can see that there is a plane of symmetry. This indicates that it is a meso compound, which is achiral and will not show optical activity.
4. **Conclusion**:
- After analyzing the structures, we conclude that the third structure is the achiral compound that will not exhibit optical activity.
### Final Answer:
- The molecule that will not show optical activity is **option C** (the third structure).
