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Chapter 7: Problem 45

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 \( 4.55 \times 10^{14} Hz \).

Step by step solution

01

Convert the wavelength to meters

Given that the wavelength is 660 nm, we need to convert it to meters before we can solve for the frequency. We know that 1 meter equals \( 10^9 \) nanometers, so we can convert as follows: \( 660\, nm \times \frac{1\, m}{10^9\, nm} = 660 \times 10^{-9}\, m = 6.6 \times 10^{-7} m \)
02

Find the frequency

Now that we know the wavelength (λ) in meters, we can use the formula \( c = νλ \) to solve for the frequency (ν). We are given the speed of light (c) as \( 3.0 \times 10^8 m/s \). Divide both sides of the equation by λ to solve for the frequency: \( ν = \frac{c}{λ} \) Plugging in the values we have: \( ν = \frac{3.0 \times 10^8\, m/s}{6.6 \times 10^{-7}\, m} \)
03

Calculate the frequency

Now, we just need to perform the division to find the frequency: \( ν ≈ \frac{3.0 \times 10^8}{6.6 \times 10^{-7}} = 4.55 \times 10^{14}\, Hz \) Therefore, the frequency of the 660 nm light used in photosynthesis is approximately \( 4.55 \times 10^{14} Hz \).

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