Question

A green leaf has a surface area of 2.05cm2 .

If solar radiation is 1090W/m2 , how many photons strike the leaf every second? Assume three significant figures and an average wavelength of 504 nm for solar radiation.

Need the answer in photons per second

Answer 1

The energy of each photon will be:

E = h x c / (L) ==> h = Planck's constant; c = speed of light; L = wavelenght of the photon

E = (6.62 x 10^-34 x 3 x 10^8 ) / (5.04 x 10^-07) ~ 3.94 x 10^-19 J

The solar power is:

1,090 W / m^2 = 0.109 W / cm^2

Since the leaf area is 2.7 cm^2, the total power hitting the leaf will be:

P(leaf) = 0.109 x 2.7 cm^2 = 0.294 W / leaf

These will be eq. to 0.294 Joules in 1 sec

If each photon has an energy of 3.94 x 10^-19 Joules, the number of photons needed to deliver this amount of Joules will be:

0.294 J = N(photons) x 3.94 x 10^-19 J

N = (29.4 / 3.94) x 10^17 ~ 7.5 x 10^17 photons.