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Chapter 2: Problem 148

Photosynthesis uses 660 -nm light to convert \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}\) into glucose and \(\mathrm{O}_{2}\). Calculate the frequency of this light.

Short Answer

Expert verified
The frequency of the 660-nm light used in photosynthesis is approximately \(4.55 \times 10^{14}\,\mathrm{Hz}\).

Step by step solution

01

Convert the Wavelength to Meters

The given wavelength of light is in nanometers, and we need to convert it into meters to be compatible with the speed of light in meters per second. To do so, use the following conversion factor: \(1\,\mathrm{m} = 10^9\,\mathrm{nm}\). So, the wavelength in meters can be calculated as: \(\lambda_\mathrm{meters} = \cfrac{660\,\mathrm{nm}}{10^9\,\mathrm{nm/m}}\).
02

Calculate the Frequency of Light

Now that we have the wavelength in meters, we can apply the formula mentioned above to determine the frequency of the light used in photosynthesis. \(f = \cfrac{c}{\lambda_\mathrm{meters}}\), Substitute the values: \(f = \cfrac{3.0 \times 10^8\,\mathrm{m/s}}{660\,\mathrm{nm} \times 10^{-9}\,\mathrm{m/nm}}\).
03

Calculate the Final Value

Perform the calculations to obtain the frequency of light: \(f = \cfrac{3.0 \times 10^8}{660 \times 10^{-9}}\), \(f = \cfrac{3.0 \times 10^8}{6.6 \times 10^{-7}}\), \(f = 4.55 \times 10^{14}\,\mathrm{Hz}\). The frequency of the 660-nm light used in photosynthesis is approximately \(4.55 \times 10^{14}\,\mathrm{Hz}\).

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