To determine which chemical reaction proves the cyclic relationship between photosynthesis and respiration, we need to identify the reactions where the products of photosynthesis are the reactants in respiration and vice versa.
Let's evaluate each option one-by-one:
### Option A
Photosynthesis: [tex]\(6 \, O_2 + 6 \, H_2O \rightarrow C_6H_{12}O_0 + 6 \, O_2\)[/tex]
- This suggests that water and oxygen directly form glucose and more oxygen. However, the byproduct should not be oxygen again; it should be glucose and oxygen or some distinct products.
### Option B
Photosynthesis: [tex]\( C_6H_{12}O_0 + O_2 \rightarrow 6 \, CO_2 + 6 \, H_2O + \text{ATP}\)[/tex]
- This suggests glucose and oxygen directly produce carbon dioxide, water, and energy. This resembles a respiration reaction rather than photosynthesis, indicating glucose breakdown.
### Option C
Photosynthesis: [tex]\(6 \, CO_2 + 6 \, H_2O \rightarrow C_6H_{12}O_6 + 6 \, O_2\)[/tex]
- (carbon dioxide + water → glucose + oxygen)
Respiration: [tex]\(C_6H_{12}O_6 + 6 \, O_2 \rightarrow 6 \, CO_2 + 6 \, H_2O + \text{ATP}\)[/tex]
- (glucose + oxygen → carbon dioxide + water + energy)
In option C, the chemical equation for photosynthesis is:
[tex]\[ 6 \, CO_2 + 6 \, H_2O \rightarrow C_6H_{12}O_6 + 6 \, O_2 \][/tex]
This shows that carbon dioxide and water are used to produce glucose and oxygen.
The chemical equation for respiration is:
[tex]\[ C_6H_{12}O_6 + 6 \, O_2 \rightarrow 6 \, CO_2 + 6 \, H_2O + \text{ATP} \][/tex]
This shows that glucose and oxygen are used to produce carbon dioxide, water, and energy (ATP).
### Conclusion
Option C shows the correct cyclic relationship, where the products of photosynthesis (glucose and oxygen) are the reactants in respiration and the products of respiration (carbon dioxide and water) are the reactants in photosynthesis.
Thus, the correct answer is:
[tex]\[ \boxed{3} \][/tex]
