Example 5.5: The Energy of a Photon

Now that we know how to calculate the wavelength and frequency of a photon, we can use this information, along with Planck's constant, to determine how much energy each photon carries. How much energy does a red photon of wavelength 630 nm have?

Solution

First, as we learned earlier, we can find the frequency of the photon:

$\displaystyle f=\frac{c}{\lambda} =\frac{3\times 10^{8}\,\text{m/s}}{630\times 10^{-9}\,\text{m}} =4.8\times 10^{14}\,\text{Hz}$

Next, we can use Planck's constant to determine the energy (remember that a Hz is the same as 1/s):

$\displaystyle E=hf =\left(6.626\times 10^{-34}\,\text{J-s}\right) \left(4.8\times 10^{14}\,\text{Hz}\text{(1/s)}\right) =3.2\times 10^{-19}\,\text{J}$

Check Your Learning

What is the energy of a yellow photon with a frequency of $5.5\times 10^{14}$ Hz?

Answer:

$\displaystyle E=hf =(6.626\times 10^{-34}\,$ J-s $\displaystyle ) \left(5.5\times 10^{14}\,\text{Hz}\right) =3.6\times 10^{-19}\,\text{J}$

Bibliography

This example is a derivative work of the Creative Commons source in [1].

[1] Andrew Fraknoi, David Morrison, and Sidney Wolff, “Example 5.5: The Energy of a Photon,” in “5.4 The Structure of the Atom,” Astronomy 2e. Houston, Texas: OpenStax, 2022. Licensed CC BY 4.0 in the original 2022 release (https://creativecommons.org/licenses/by/4.0/). Changes: converted to LaTeX and separated from its parent section as a standalone PhysicsLibrary example. Access for free at https://openstax.org/books/astronomy-2e/pages/1-introduction. Section source: https://openstax.org/books/astronomy-2e/pages/5-4-the-structure-of-the-atom.

"example of structure of the atom: energy of a photon" is owned by bloftin.
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