Question

A green leaf has a surface area of 2.05 cm2.

If solar radiation is 1170 W/m2 , how many photons strike the leaf every second? Assume three significant figures and an average wavelength of 504 nm for solar radiation.

Express your answer using three significant figures.

N =

photons per second

Answer 1

First find the energy of a single photon with the wavelength of: 504 nm
Use E=hc/wavelength
E = (6.62 x 10^-34 x 3 x 10^8)/504 x 10^-9
E = 3.94 x 10^-19 J

A power of 1170 Watts means 1170 Joules per second
Therefore,
1170 Joules of energy per second will be given by n, photons per second
n = 1170/3.94 x 10^-19
n =2.97 x 10^21 photons

Therefore,
2.97x 10^21 photons are hitting 1 square m of solar panel per second.
1m^2 = 100cm x 100 cm = 10^4 cm^2
therefore
10^4 cm^2 receives 2.97 x 10^21 photons/sec
1cm^2 receives 2.97 x 10^21/10^4 photons/sec
1cm^2 receives 2.97 x 10^17 photons/sec
Therefore,
2.05 cm^2 = 2.07 x 2.97 x 10^17 photons/sec
2.05 cm^2 = 6.08 x 10^17 photons/sec

The green leaf receives 6.08 x 10^17 photons per second.