Suppose there were plants that had a high concentration of Chlorophyll b but lacked chlorophyll a, would it carry out photosynthesis? Then why do plants have chlorophyll b and other accessory pigments?
Chlorophyll a molecules act as antenna molecules. They get excited by absorbing light and emit electrons during cyclic and non-cyclic photophosphorylations. They form the reaction centres for both photosystems I and II. Chlorophyll b and other photosynthetic pigments such as carotenoids and xanthophylls act as accessory pigments. Their role is to absorb energy and transfer it to chlorophyll a. Carotenoids and xanthophylls also protect the chlorophyll molecule from photo-oxidation.
Therefore, chlorophyll a is essential for photosynthesis.
If any plant were to lack chlorophyll a and contain a high concentration of chlorophyll b, then this plant would not undergo photosynthesis.