Final Answer:
The answer of the given statement that " this arc remain visible for a long time" is c) Slow diffusion rate
Explanation:
In the Ouchterlony assay, the formation of a sharp precipitin arc between antigen and antiserum is influenced by various factors. The key reason the arc remains visible for a long time is the slow diffusion rate.
During the assay, antigen and antibody diffuse through the gel medium at a rate that is influenced by factors like temperature and the concentration of agarose or agar in the gel. If the diffusion rate is slow, the antigen and antibody have more time to interact and form a distinct precipitin arc. This allows for a clear visualization of the reaction.
Options (a) High antibody concentration and (b) Low temperature may affect the intensity of the reaction, but they are not directly related to the longevity of the visible precipitin arc. Option (d) Insufficient antigen-antibody binding would likely result in a weaker or incomplete precipitin arc rather than influencing its duration.
Therefore, in the context of the Ouchterlony assay, the c) slow diffusion rate is the critical factor contributing to the prolonged visibility of the precipitin arc.