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 three significant figures and an average wavelength of 504 nm for solar radiation.

Verified step by step guidance

1. Convert the surface area of the leaf from cm² to m² by using the conversion factor: 1 cm² = 0.0001 m².
2. Calculate the total power of solar radiation striking the leaf by multiplying the solar radiation intensity (1000 W/m²) by the leaf's surface area in m².
3. Use the energy of a photon formula, \( E = \frac{hc}{\lambda} \), where \( h \) is Planck's constant (6.626 \(\times\) 10^{-34} \(\text{ J s}\)), \( c \) is the speed of light (3.00 \(\times\) 10^8 \(\text{ m/s}\)), and \( \lambda \) is the wavelength in meters (convert 504 nm to meters).
4. Calculate the number of photons by dividing the total power (in watts) by the energy of a single photon (in joules).
5. Ensure the final answer is expressed with three significant figures.

Key Concepts

Photon Energy

The energy of a photon is determined by its wavelength, given by the equation E = hc/λ, where E is energy, h is Planck's constant (6.626 x 10^-34 J·s), c is the speed of light (3.00 x 10^8 m/s), and λ is the wavelength in meters. For a wavelength of 504 nm, this relationship allows us to calculate the energy of a single photon striking the leaf.

Solar Radiation Intensity

Solar radiation intensity, measured in watts per square meter (W/m²), indicates the power received per unit area. In this case, an intensity of 1000 W/m² means that each square meter of the leaf receives 1000 joules of energy every second. This value is crucial for determining the total energy incident on the leaf's surface area.

Surface Area Conversion

To calculate the total energy striking the leaf, the surface area must be converted from cm² to m². Since 1 m² equals 10,000 cm², a leaf with a surface area of 2.50 cm² corresponds to 0.00025 m². This conversion is essential for accurately applying the solar radiation intensity to find the total energy received by the leaf.