To determine the number of photons that strike the leaf every second, we need to use the formula:
Number of photons = (Power / Energy per photon) x Leaf area,
where:
- Power is the solar radiation (1120 W/m^2),
- Energy per photon is the energy associated with each photon,
- Leaf area is the surface area of the green leaf (2.40 cm^2).
To find the energy per photon, we can use Planck's equation:
Energy per photon = Planck's constant ร speed of light / wavelength,
where:
- Planck's constant (h) is approximately 6.63 ร 10^-34 Jยทs,
- Speed of light (c) is approximately 3 ร 10^8 m/s,
- Wavelength is the average wavelength of solar radiation (504 nm = 504 ร 10^-9 m).
Let's plug in the values and calculate:
Energy per photon = (6.63 ร 10^-34 Jยทs) ร (3 ร 10^8 m/s) / (504 ร 10^-9 m)
โ 3.94 ร 10^-19 J.
Converting the leaf area from cm^2 to m^2:
Leaf area = 2.40 cm^2 โ 2.40 ร 10^-4 m^2.
Now we can substitute all the values into the initial formula:
Number of photons = (1120 W/m^2 / 3.94 ร 10^-19 J) ร (2.40 ร 10^-4 m^2)
โ 6.79 ร 10^17 photons.
Therefore, approximately 6.79 ร 10^17 photons strike the green leaf every second under the given conditions.