In terms of organisms, photosynthesis occurs in autotrophes that contain the green pigment chlorophyll. This would include the entire plant kingdom, half of the Protista (the algae), & half the Moneran Kingdom (the blue-green algae).
A standard twin mattress is 39 by 75 inches. A king is 76 by 80 inches. This means that a headboard for a king bed is going to be about 76 inches or wider, plenty wide enough to go along the length of a twin bed. Headboards are often slightly wider than the bed for which they are made.
Both sizes are equal in estimated length (75 inches) but differ in width (53 inches for double/full size and 37 inches for the standard twin). A variant of the twin or standard size, the extra-long twin, is narrower compared to the two sizes with 80 inches in length.