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QuestionFind the energy of a photon with a wavelength of 999μm999 \mu \mathrm{m}.

Studdy Solution

STEP 1

Assumptions1. The wavelength of the photon is 999μm999 \mu m . We will use the formula for the energy of a photon, which is given by Planck's equation =hcλ = \frac{hc}{\lambda}
3. The Planck's constant (h) is 6.62607004×10−34mkg/s6.62607004 \times10^{-34} m^ kg / s
4. The speed of light (c) is 3.00×108m/s3.00 \times10^8 m/s

STEP 2

First, we need to convert the wavelength from micrometers to meters, because the constants in Planck's equation are given in terms of meters.
λ=999μm=999×10−6m\lambda =999 \mu m =999 \times10^{-6} m

STEP 3

Now, we can substitute the values of the Planck's constant (h), the speed of light (c), and the wavelength (λ) into Planck's equation to calculate the energy of the photon.
=hcλ=(6.62607004×10−34m2kg/s)(3.00×108m/s)999×10−6m = \frac{hc}{\lambda} = \frac{(6.62607004 \times10^{-34} m^2 kg / s)(3.00 \times10^8 m/s)}{999 \times10^{-6} m}

STEP 4

Perform the calculation to find the energy of the photon.
=(6.62607004×10−34m2kg/s)(3.00×108m/s)999×10−6m=1.98644542×10−22J = \frac{(6.62607004 \times10^{-34} m^2 kg / s)(3.00 \times10^8 m/s)}{999 \times10^{-6} m} =1.98644542 \times10^{-22} JThe energy of the photon is 1.98644542×10−22J1.98644542 \times10^{-22} J.

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