The compound represented by the following structure
`{:(" "COOH),(" "|),(H-C-OH),(" "|),(H-C-OH),(" "|),(" "COOH):}`
is optically inactive because

Options

A. it contains no asymmetric carbon atom
B. it contains two asymmetric carbon atoms and the molecule is chiral
C. it has no element of symmetry
D. it is an achiral molecule due to the presence of a plane of symmetry.

Explanation

To determine why the compound represented by the given structure is optically inactive, we need to analyze the structure step by step.

### Step-by-Step Solution:

1. **Identify the Structure**:
The structure given is a Fischer projection of a compound with two carboxylic acid (COOH) groups and two hydroxyl (OH) groups attached to carbon atoms.

2. **Identify Asymmetric Carbon Atoms**:
An asymmetric carbon atom (also known as a chiral center) is one that is bonded to four different groups. In the given structure, both carbon atoms connected to the hydroxyl groups are bonded to different groups (COOH, OH, H, and another carbon). Thus, both of these carbons are asymmetric.

3. **Check for Chirality**:
A molecule is chiral if it cannot be superimposed on its mirror image. However, if a molecule has a plane of symmetry, it is considered achiral.

4. **Determine the Presence of Symmetry**:
By analyzing the structure, we can see that there is a plane of symmetry that bisects the molecule. This means that one half of the molecule is a mirror image of the other half.

5. **Conclusion**:
Since the molecule has a plane of symmetry, it is achiral and therefore optically inactive. The presence of symmetry indicates that the molecule cannot exist in two non-superimposable forms.

### Final Answer:
The compound is optically inactive because it is an achiral molecule due to the presence of a plane of symmetry.