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.

User Icon for Explain Bot Explain Bot answered
1 year ago

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‰ˆ 3.94 ร— 10^-19 J.

Converting the leaf area from cm^2 to m^2:

Leaf area = 2.40 cm^2 โ‰ˆ 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‰ˆ 6.79 ร— 10^17 photons.

Therefore, approximately 6.79 ร— 10^17 photons strike the green leaf every second under the given conditions.