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.