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Chapter 36: Problem 61

A photovoltaic device uses monochromatic light of wavelength 700 . \(\mathrm{nm}\) that is incident normally on a surface of area \(10.0 \mathrm{~cm}^{2}\). Calculate the photon flux rate if the light intensity is \(0.300 \mathrm{~W} / \mathrm{cm}^{2}\).

Short Answer

Expert verified
Answer: The photon flux rate is approximately \(1.06 \times 10^{19}\) photons per second.

Step by step solution

01

Calculate the energy of a single photon

Using the wavelength of the light, we can determine the energy of a single photon using the Plank's equation: \(E = h \cdot f\) where \(E\) is the energy of the photon, \(h\) is the Planck's constant (\(6.63 \times 10^{-34}\, \mathrm{Js}\)), and \(f\) is the frequency of the light. To find the frequency, we can use the speed of light formula: \(c = f \cdot \lambda\) where \(c\) is the speed of light (\(3 \times 10^8\, \mathrm{m/s}\)), \(f\) is the frequency, and \(\lambda\) is the wavelength. We'll rearrange this equation to solve for \(f\): \(f = \frac{c}{\lambda}\)
02

Convert the wavelength to meters

The given wavelength is in nanometers (nm), but we need to convert it to meters (m) to work with the other units in this exercise. To convert nanometers to meters, multiply by \(10^{-9}\): \(\lambda = 700\, \mathrm{nm} \cdot 10^{-9}\, \mathrm{m/nm} = 7 \times 10^{-7}\, \mathrm{m}\)
03

Calculate the frequency of the light

Now that we have the wavelength in meters, we can find the frequency of the light using the speed of light formula: \(f = \frac{3 \times 10^8\, \mathrm{m/s}}{7 \times 10^{-7}\, \mathrm{m}} \approx 4.29 \times 10^{14}\, \mathrm{Hz}\)
04

Calculate the energy of a single photon

Now, we can calculate the energy of a single photon using the calculated frequency and Planck's equation: \(E = h \cdot f = (6.63 \times 10^{-34}\, \mathrm{Js}) \cdot (4.29 \times 10^{14}\, \mathrm{Hz}) \approx 2.84 \times 10^{-19}\, \mathrm{J}\)
05

Calculate the total incident power on the surface

We are given the light intensity, \(I = 0.300\, \mathrm{W/cm}^2\). We can find the total incident power on the surface by multiplying the light intensity by the surface area: \(P = I \cdot A = (0.300\, \mathrm{W/cm}^2) \cdot (10.0\, \mathrm{cm}^2) = 3\, \mathrm{W}\)
06

Calculate the photon flux rate

Finally, we can calculate the photon flux rate by dividing the total incident power by the energy of a single photon: \(\Phi = \frac{P}{E} = \frac{3\, \mathrm{W}}{2.84 \times 10^{-19}\, \mathrm{J}} \approx 1.06 \times 10^{19}\, \mathrm{photons/s}\) The photon flux rate is approximately \(1.06 \times 10^{19}\) photons per second.

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