Not all plants have chlorophyll b, and it is less abundant than a. Chlorophyll a does everything than b does, but not vice versa, so plants can survive with a only. Having b in addition to a means only that a plant can increase it's energy production :-)

Chlorophyll a is universal while chlorophyll b, c, d and e are optional. For instance in brown algae chlorophyll c is present in place of chlorophyll b. Similarly in red algae chlorophyll d is present in place of chlorophyll b. Hence chlorophyll a can be detected in absence of chlorophyll b.

Chlorina mutants have littleor no Chlb. Peripheral antennas assembly is required to cope with high lòight but does not affect vitality. You should test by HPLC using specific columns among different sources of the plant in use refs in http://onlinelibrary.wiley.com/doi/10.1111/j.1399-3054.1992.tb05817.x/abstract