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QuestionWhat is the frequency in hertz (Hz) of a photon with a wavelength of 2.86×10−72.86 \times 10^{-7} m?

Studdy Solution

STEP 1

Assumptions1. The energy of the photon is given as 1.97×10−191.97 \times10^{-19} J. The wavelength of the photon is given as .86×10−7.86 \times10^{-7} m3. The speed of light in a vacuum is a constant, c=3.00×108c =3.00 \times10^{8} m/s4. The relationship between energy, frequency, and Planck's constant is given by the equation =h⋅f = h \cdot f, where $$ is the energy of the photon, $h$ is Planck's constant ($6.626 \times10^{-34}$ J$\cdot$s), and $f$ is the frequency of the photon5. The relationship between wavelength, frequency, and the speed of light is given by the equation $c = \lambda \cdot f$, where $c$ is the speed of light, $\lambda$ is the wavelength of the photon, and $f$ is the frequency of the photon

STEP 2

First, we need to find the frequency of the photon. We can do this by rearranging the equation =h⋅f = h \cdot f to solve for ff.
f=hf = \frac{}{h}

STEP 3

Now, plug in the given values for the energy of the photon and Planck's constant to calculate the frequency.
f=1.97×10−19 J6.626×10−34 J⋅sf = \frac{1.97 \times10^{-19} \, \mathrm{J}}{6.626 \times10^{-34} \, \mathrm{J} \cdot \mathrm{s}}

STEP 4

Calculate the frequency of the photon.
f=1.97×10−196.626×10−34=2.97×1014 Hzf = \frac{1.97 \times10^{-19}}{6.626 \times10^{-34}} =2.97 \times10^{14} \, \mathrm{Hz}The frequency of the photon is 2.97×10142.97 \times10^{14} Hz.

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