A green leaf has a surface area of 2.40 cm^2.
If solar radiation is 1120 W/m^2, how many photons strike the leaf every second? Assume three significant figures and an average wavelength of 504 nm for solar radiation.
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 × speed of light / wavelength,
where:
- Planck's constant (h) is approximately 6.63 × 10^-34 J·s,
- Speed of light (c) is approximately 3 × 10^8 m/s,
- Wavelength is the average wavelength of solar radiation (504 nm = 504 × 10^-9 m).
Let's plug in the values and calculate:
Energy per photon = (6.63 × 10^-34 J·s) × (3 × 10^8 m/s) / (504 × 10^-9 m)
≈ 3.94 × 10^-19 J.
Converting the leaf area from cm^2 to m^2:
Leaf area = 2.40 cm^2 ≈ 2.40 × 10^-4 m^2.
Now we can substitute all the values into the initial formula:
Number of photons = (1120 W/m^2 / 3.94 × 10^-19 J) × (2.40 × 10^-4 m^2)
≈ 6.79 × 10^17 photons.
Therefore, approximately 6.79 × 10^17 photons strike the green leaf every second under the given conditions.