(a) Find a symbolic expression for the wavelength λof a photon in terms of its energy E, Planck'

Name: Problem 4, Chapter 22: College Physics
Uploaded: 2019-12-10T14:21:28-08:00
Duration: 2 min 17 s
Channel: Zachary Warner
Description: (a) Find a symbolic expression for the wavelength λof a photon in terms of its energy E, Planck's constant h, and the speed of light c, (b) What does the equation say about the wavelengths of higher-energy photons?

step 1 Our question for Part A asks us to find a symbolic expression for the wavelength lambda of a pho

Question

(a) Find a symbolic expression for the wavelength $\lambda$ of a photon in terms of its energy $E,$ Planck's constant $h,$ and the speed of light $c,$ (b) What does the equation say about the wavelengths of higher-energy photons?

   (a) Find a symbolic expression for the wavelength $\lambda$ of a photon in terms of its energy $E,$ Planck's constant $h,$ and the speed of light $c,$ (b) What does the equation say about the wavelengths of higher-energy photons?

College Physics

Raymond A. Serway,… 11th Edition

Chapter 22, Problem 4

Instant Answer

Solved by Expert Zachary Warner

12/10/2019

Step 1

Step 1: The energy of a photon is given by the equation $E = h \nu$, where $E$ is the energy, $h$ is Planck's constant, and $\nu$ is the frequency of the photon. Show more…

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(a) Find a symbolic expression for the wavelength $\lambda$ of a photon in terms of its energy $E,$ Planck's constant $h,$ and the speed of light $c,$ (b) What does the equation say about the wavelengths of higher-energy photons?

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Key Concepts

Photon Energy-Wavelength Relationship

This fundamental concept in quantum mechanics links a photon's energy to its wavelength. It starts from the relation E = hf, where h is Planck's constant and f is frequency, and uses the connection between frequency and wavelength (f = c/?) to derive the expression E = hc/?. Rearranging this yields ? = hc/E, expressing the photon's wavelength in terms of its energy.

Inverse Proportionality

The equation ? = hc/E reveals an inverse relationship between a photon's energy and its wavelength. As the energy increases, the wavelength decreases, which means that higher-energy photons correspond to shorter wavelengths. This inverse relationship is central to understanding phenomena in areas such as electromagnetic radiation and quantum physics.

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