Question

A sodium flame has a characteristic yellow color due to emission of light of wavelength $589 \mathrm{nm}$. What is the mass equivalence of one photon with this wavelength $\left(1 \mathrm{~J}=1 \mathrm{~kg} \cdot \mathrm{m}^{2} / \mathrm{s}^{2}\right) ?$

Name: Problem 43, Chapter 7: CHEMISTRY: The Molecular Nature of Matter and Change
Uploaded: 2021-06-03T12:07:47-08:00
Duration: 2 min 53 s
Channel: Nicole Smina
Description: A sodium flame has a characteristic yellow color due to emission of light of wavelength 589 nm. What is the mass equivalence of one photon with this wavelength (1 J=1 kg ·m^2 / s^2) ?

   A sodium flame has a characteristic yellow color due to emission of light of wavelength $589 \mathrm{nm}$. What is the mass equivalence of one photon with this wavelength $\left(1 \mathrm{~J}=1 \mathrm{~kg} \cdot \mathrm{m}^{2} / \mathrm{s}^{2}\right) ?$

CHEMISTRY: The Molecular Nature of Matter and Change

Martin S.… 9th Edition

Chapter 7, Problem 43

Instant Answer

Solved by Expert Nicole Smina

06/03/2021

Step 1

Step 1: We start by using the equation for the energy of a photon, which is given by $E = h \cdot c / \lambda$, where $E$ is the energy of the photon, $h$ is Planck's constant, $c$ is the speed of light, and $\lambda$ is the wavelength of the light. Show more…

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A sodium flame has a characteristic yellow color due to emission of light of wavelength $589 \mathrm{nm}$. What is the mass equivalence of one photon with this wavelength $\left(1 \mathrm{~J}=1 \mathrm{~kg} \cdot \mathrm{m}^{2} / \mathrm{s}^{2}\right) ?$

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Key Concepts

Mass-Energy Equivalence

Mass-energy equivalence is the principle expressed by Einstein's famous equation E = mc², which establishes that mass and energy are interchangeable. In the context of photon energy, even though a photon is massless in terms of rest mass, its energy can be associated with an equivalent mass using the relation m = E/c². This concept bridges the gap between energy and matter, showing that any energy, including that of a photon, has a corresponding mass equivalence.

Photon Energy

Photons are quantized packets of electromagnetic energy, and the energy of a photon is directly related to its wavelength or frequency. This relationship is given by the equation E = hc/?, where E is the energy, h is Planck’s constant, c is the speed of light, and ? is the wavelength. This formula shows that shorter wavelengths (or higher frequencies) correspond to higher photon energy.

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