How much energy is available in visible light? How much energy does sunlight deliver to Earth? How efficient are plants at converting light energy into chemical energy? The answers to these questions provide an important backdrop to the subject of photosynthesis.

Each quantum or photon of light has energy hv, where h is Planck’s constant (6.6 × 10^–37 kJ sec/photon) and v is the frequency in sec–1. The frequency of light is equal to c/λ, where c is the speed of light (3.0 × 10¹⁷ nm/ sec) and λ is the wavelength in nm. Thus, the energy (E) of a photon is

E = hv = hc/λ

A. Calculate the energy of a mole of photons (6 × 10²³ photons/mole) at 400 nm (violet light), at 680 nm (red light), and at 800 nm (near-infrared light).

B. Bright sunlight strikes Earth at the rate of about 1.3 kJ/sec per square meter. Assuming for the sake of calculation that sunlight consists of monochromatic light of wavelength 680 nm, how many seconds would it take for a mole of photons to strike a square meter?

C. Assuming that it takes eight photons to fix one molecule of CO₂ as carbohydrate under optimal conditions (8–10 photons is the currently accepted value), calculate how long it would take a tomato plant with a leaf area of 1 square meter to make a mole of glucose from CO₂.

Assume that photons strike the leaf at the rate calculated above and, furthermore, that all the photons are absorbed and used to fix CO₂.

D. If it takes 468 kJ/mole to fix a mole of CO₂ into carbohydrate, what is the efficiency of conversion of light energy into chemical energy after photon capture? Assume again that eight photons of red light (680 nm) are required to fix one molecule of CO₂.