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Chapter 27: Problem 3

Find the (a) wavelength and (b) frequency of a 3.1 -eV photon.

Short Answer

Expert verified
Answer: The wavelength of the 3.1 eV photon is 4.004 × 10^{-7} m or 400.4 nm, and the frequency is 7.491 × 10^{14} Hz.

Step by step solution

01

Convert energy from eV to J

To convert the energy of the photon from electron volts to joules, we use the following conversion factor: 1 eV = 1.602 × 10^{-19} J. So, E (J) = 3.1 eV × (1.602 × 10^{-19} J/eV) = 4.9662 × 10^{-19} J.
02

Use the energy equation to find the frequency

Using the energy equation E = hf, where h is the Planck's constant (h = 6.626 × 10^{-34} Js), we can solve for the frequency as follows: f = E/h = (4.9662 × 10^{-19} J) / (6.626 × 10^{-34} Js) = 7.491 × 10^{14} Hz.
03

Use the speed of light equation to find the wavelength

Since the speed of light c = λf, we can find the wavelength (λ) of the photon by solving for λ: λ = c/f, where c = 3 × 10^8 m/s (the speed of light in a vacuum). Thus, λ = (3 × 10^8 m/s) / (7.491 × 10^{14} Hz) = 4.004 × 10^{-7} m. So, the (a) wavelength of the 3.1-eV photon is 4.004 × 10^{-7} m or 400.4 nm, and the (b) frequency is 7.491 × 10^{14} Hz.

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