Question

A green leaf has a surface area of 2.50 cm2. If solar radiation is 1000 W/m2, how many photons strike the leaf every second? Assume 3 sig figs and average wavelength being 504 nm for solar radiation.

Answer 1

The energy receie by leaf will be

1000 W/m2

We can express it as 1000 J / m² sec

Let us convert m2 to cm2

So the energy recieved by leaf = 1000 J / 10^4 cm^2 per second

So energy received in 1cm^2 = 0.1 Joules / second
Hence radiation received on 2.5 cm^2 = 0.1 X 2.5 = 0.25 Joules / second
We know that

Where c = speed of light = 3 X 10^8 m / seconds

h = planck's constant = 6.62 X 10^-34

The energy carried by photon = 6.62 X 10^-34 X 3 X 10^8 / 504 X 10^-9

Energy of photon = 0.0394 X 10^-17 joules

So number of photons = Total energy / energy of photons = 0.25 Joules / 0.0394 X 10^-17 joules

Number of photons = 6.345 X 10^17 photons / second