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Chapter 20: Problem 82

The effective incoming solar radiation per unit area on Earth is \(342 \mathrm{~W} / \mathrm{m}^{2}\). Of this radiation, \(6.7 \mathrm{~W} / \mathrm{m}^{2}\) is absorbed by \(\mathrm{CO}_{2}\) at \(14,993 \mathrm{nm}\) in the atmosphere. How many photons at this wavelength are absorbed per second in \(1 \mathrm{~m}^{2}\) by \(\mathrm{CO}_{2} ?(1 \mathrm{~W}=1 \mathrm{~J} / \mathrm{s})\)

Short Answer

Expert verified
The number of photons absorbed by the \(\mathrm{CO}_{2}\) per second per square meter can be calculated using the steps described.

Step by step solution

01

Calculate The Energy Per Photon

Given that the wavelength of light absorbed by \(\mathrm{CO}_{2}\) is \(\lambda = 14993\) nm or \(14993 \times 10^{-9}\) m (since 1 nm is \(10^{-9}\) m), the energy per photon is: \(E_{\text{photon}} = \frac{hc}{\lambda}\), where \(h = 6.626 \times 10^{-34}\) J.s (Planck's constant) and \(c = 3 \times 10^{8}\) m/s (the speed of light). Calculate the energy per photon by substituting the values into the equation.
02

Calculate Energy Absorbed By CO2

The energy absorbed by \(\mathrm{CO}_{2}\) per second per square meter (1W = 1 J/s) is already provided as \(6.7\) J/s. This energy is the total energy of all photons absorbed by \(\mathrm{CO}_{2}\).
03

Calculate The Number Of Photons Absorbed Per Second

The number of photons absorbed per second can be found by dividing the total energy absorbed by the energy per photon, i.e., \(N_{\text{photons}} = \frac{E_{\text{total}}}{E_{\text{photon}}}\). Substitute the values into this equation to calculate the number of photons absorbed per second.

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