Can we assume that there is a complete one to one overlap between absorption spectrum of chlorophyll a and the action spectrum of photosynthesis? ??

no there is not a complete one to one overlap between the absorption spectrum of chlorophyll a and the action spectrum of photosynthesis because there are other pigments also in chloroplast (like chlorophyll a , xanthophylls and carotenoids ) which are related for absorption. hope this will help you :-)

NO! Although the curves of action spectrum are majorly affected by the chief role of Chlorophyll a. It is also influenced by absorption spectrums of Chlorophyll b, carotenoids, xanthophylls as they are also responsible for rate of Photosynthesis at some point...Action spectrum is an overall analysis of the rate of Photosynthesis at different wavelengths and not just about Chlorophyll a....To be more clear about the question provided in the last paragraph of ncert. According to higher references. Action spectrum curve is the average taken for the individual curves which we see in 13.3a for all 4 pigments as the amount of light absorbed is directly proportional to the rate of Photosynthesis (refer graph 13.3c now ) Aarohi Rajwar