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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 脳 10^{-7} m or 400.4 nm, and the frequency is 7.491 脳 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 脳 10^{-19} J. So, E (J) = 3.1 eV 脳 (1.602 脳 10^{-19} J/eV) = 4.9662 脳 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 脳 10^{-34} Js), we can solve for the frequency as follows: f = E/h = (4.9662 脳 10^{-19} J) / (6.626 脳 10^{-34} Js) = 7.491 脳 10^{14} Hz.
03

Use the speed of light equation to find the wavelength

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

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Most popular questions from this chapter

A Compton scattering experiment is performed using an aluminum target. The incident photons have wavelength \(\lambda\). The scattered photons have wavelengths \(\lambda^{\prime}\) and energies \(E\) that depend on the scattering angle \(\theta.\) (a) At what angle \(\theta\) are scattered photons with the smallest energy detected? (b) At this same scattering angle \(\theta,\) what is the ratio \(\lambda^{\prime} / \lambda\) for \(\lambda=10.0 \mathrm{pm} ?\)
How much energy is required to ionize a hydrogen atom initially in the \(n=2\) state?
Suppose that you have a glass tube filled with atomic hydrogen gas (H, not \(\mathrm{H}_{2}\) ). Assume that the atoms start out in their ground states. You illuminate the gas with monochromatic light of various wavelengths, ranging through the entire IR, visible, and UV parts of the spectrum. At some wavelengths, visible light is emitted from the \(\mathrm{H}\) atoms. (a) If there are two and only two visible wavelengths in the emitted light, what is the wavelength of the incident radiation? (b) What is the largest wavelength of incident radiation that causes the \(\mathrm{H}\) atoms to emit visible light? What wavelength(s) is/are emitted for incident radiation at that wavelength? (c) For what wavelengths of incident light are hydrogen ions \(\left(\mathrm{H}^{+}\right)\) formed?
By directly substituting the values of the fundamental constants, show that the Bohr radius \(a_{0}=\hbar^{2} /\left(m_{\mathrm{e}} k e^{2}\right)\) has the numerical value \(5.29 \times 10^{-11} \mathrm{m}.\)
Use the Bohr theory to find the energy necessary to remove the electron from a hydrogen atom initially in its ground state.
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