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QuestionFind the frequency of light with a wavelength of 428 nm428 \mathrm{~nm}. Round to 3 significant figures in scientific notation.

Studdy Solution

STEP 1

Assumptions1. The wavelength of the light is428 nm (nanometers) . We will use the speed of light as a constant, which is approximately 3.00×1083.00 \times10^8 m/s3. We will use the formula for the frequency of a wave, which is given by f=cλf = \frac{c}{\lambda}, where ff is the frequency, cc is the speed of light, and λ\lambda is the wavelength.

STEP 2

First, we need to convert the wavelength from nanometers to meters, as the speed of light is given in meters per second. We can do this by multiplying the wavelength by 10−910^{-9}.
λ=428 nm×10−9 m/nm\lambda =428 \, nm \times10^{-9} \, m/nm

STEP 3

Calculate the wavelength in meters.
λ=428×10−9 m=.28×10−7 m\lambda =428 \times10^{-9} \, m =.28 \times10^{-7} \, m

STEP 4

Now that we have the wavelength in meters, we can substitute the values into the formula for the frequency of a wave.
f=cλf = \frac{c}{\lambda}

STEP 5

Substitute the values for the speed of light and the wavelength into the formula.
f=3.00×108 m/s4.28×10−7 mf = \frac{3.00 \times10^8 \, m/s}{4.28 \times10^{-7} \, m}

STEP 6

Calculate the frequency of the light.
f=3.00×1084.28×10− s−1=.01×1014 s−1f = \frac{3.00 \times10^8}{4.28 \times10^{-}} \, s^{-1} =.01 \times10^{14} \, s^{-1}The frequency of the light with a wavelength of428 nm is .01×1014.01 \times10^{14} Hz.

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