Can photosynthesis, in plants, occur with artificial light? If so, can you use LED light?
Yes they will and yes you can use LEDs. BUT.... different plants have different lighting requirements. They sell several different types of LEDs for plants, but for plants that would grow outside in full sun most growers would consider them inferior to more intense lighting, but they seem to offer good light output for wattage used and they can be had with different spectrum's designed to be more efficient than others. One brand that is popular is the 90watt. UFO design. They also have a 300 watt type. Depending on what your growing you might want to add supplemental lighting of a different type too.
