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QuestionFind the frequency of light with a wavelength of 576 nm576 \mathrm{~nm}. Round to 3 significant figures, use scientific notation if needed.

Studdy Solution

STEP 1

Assumptions1. The wavelength of the light is576 nm (nanometers). . We will use the speed of light in a vacuum, which is approximately 3.00×1083.00 \times10^8 meters per second.
3. We will use the formula for the relationship between the speed of light (c), frequency (f), and wavelength (λ): c=f×λc = f \times λ.
4. We are asked to find the frequency, so we will rearrange the formula to solve for f f=c/λf = c / λ.

STEP 2

First, we need to convert the wavelength from nanometers to meters, since the speed of light is given in meters per second. There are 1×1091 \times10^9 nanometers in a meter, so we divide the given wavelength by this factor.
λ=576 nm/(1×109 nm/m)λ =576 \, nm / (1 \times10^9 \, nm/m)

STEP 3

Calculate the wavelength in meters.
λ=576 nm/(1×109 nm/m)=5.76×10−7 mλ =576 \, nm / (1 \times10^9 \, nm/m) =5.76 \times10^{-7} \, m

STEP 4

Now that we have the wavelength in meters, we can substitute the values of the speed of light and the wavelength into the formula to calculate the frequency.
f=c/λ=(3.00×108 m/s)/(.76×10−7 m)f = c / λ = (3.00 \times10^8 \, m/s) / (.76 \times10^{-7} \, m)

STEP 5

Calculate the frequency.
f=(3.00×108 m/s)/(5.76×10−7 m)=5.21×1014 Hzf = (3.00 \times10^8 \, m/s) / (5.76 \times10^{-7} \, m) =5.21 \times10^{14} \, HzThe frequency of the light with a wavelength of576 nm is 5.21×10145.21 \times10^{14} Hz.

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