Photon Energy - The Energy of Light Particles
Video - Photoelectric Effect and The Einstein Formula Simply Explained
In quantum physics it has turned out that in many experiments it makes sense to consider light not as a wave but as a stream of many particles. Such a light particle is called a photon.
The energy of a photon is determined by the light frequency \( f \). If we consider the light wave-like, then the frequency indicates how often the light wave oscillates per second. The unit of frequency is \( [f] = \frac{1}{\mathrm s}, \) though this is noted somewhat more compactly as \( \frac{1}{\mathrm s} = \mathrm{Hz} \). "Hz" stands for "Hertz" - in honor of a physicist named Heinrich Hertz.
An important insight of quantum mechanics was that the energy of a photon is connected with the so-called Planck's constant \( h \) - with one of the most important constants of physics! It has always the same value \( h ~=~ 6.626 \cdot 10^{-34} \, \mathrm{Js} \). As you can see, it is incredibly small and has the unit \( [h] = \mathrm{Js} \). "Js" stands for "Joule times second", where \( \mathrm{J} \) (Joule) is the unit of energy.
With the help of the Planck's constant and the light frequency you can easily answer the question about the energy of a photon:
Unit of energy \( W_{\text p} \) is Joule (J).
The larger the light frequency \( f \), the larger is the energy of a photon.
The formula 1
tells you only how large the energy of a single photon is. If you want to find out how large the energy of many photons is, you have to determine their number and multiply it by the energy of a single photon 1
. Thus, if \( n \) photons hit a capacitor plate, for example, the total energy arriving at the plate is given by:
Sometimes you know instead of the light frequency \( f \) the corresponding wavelength \( \lambda \) (pronunciation: "Lamda"). Once you know either the frequency or the wavelength, you can easily convert them into each other, because they are related by the speed of light \( c \):
The wavelength, as the name implies, is the distance from one crest to another crest of the light wave. And which unit has the wavelength? So that the unit of the (light) speed \( [c] = \frac{\text m}{\text s} \) in the equation 3
is correct, the wavelength must have the unit \( [\lambda] = \text{m} \), because the frequency has the unit \( [f] = \frac{1}{\text s} \)!
The cool thing about it is: You don't have to determine the speed of light at all. Why not? Because the speed of light is a constant just like the Planck's constant! In a medium (in your case it is air or vacuum) it always has the same value:
&~\approx~ 3 \cdot 10^{8} \, \frac{\mathrm m}{\mathrm s} \end{align} $$
From the instruction manual of your laser pointer you read that the light emitted by the laser pointer has a wavelength \( \class{green}{\lambda} ~=~ \class{green}{500 \, \mathrm{nm}} \) (\( \mathrm{nm} \) stands for "nanometer", so \(10^{-9} \, \mathrm{m}\)).
You have just learned that you can easily determine the frequency \( \class{green}{f} \) from the wavelength. So you use the formula 3
rearranged for frequency:
&~=~ \class{green}{ 6 \cdot 10^{14} \, \text{Hz} } \end{align} $$
Using formula 3
, which gives the relation between the light frequency and light wavelength, you can express the photon energy 1
also using the wavelength:
The larger the light wavelength \( \lambda \), the smaller is the energy of a photon.
What color do photons have?
If you hear something like "wavelength of green light", then the "green" refers to a certain light frequency or light wavelength. Depending on the wavelength / frequency, you perceive the light in a different color.
| Light wavelength | Light frequency | Energy of a photon |
|---|---|---|
| 575 nm | 5.2 × 1014 Hz | 3.5 × 10-19 J |
| 546 nm | 5.5 × 1014 Hz | 3.6 × 10-19 J |
| 435 nm | 6.9 × 1014 Hz | 4.6 × 10-19 J |
| 400 nm | 7.5 × 1014 Hz | 5 × 10-19 J |
| 365 nm (UV light) | 8.2 × 1014 Hz | 5.4 × 10-19 J |
Take an interference filter, which filters out all colors except the yellow color. The yellow color has the wavelength \( \lambda = 575 \, \mathrm{nm} \). Written out the wavelength of the yellow light is: \( \lambda = 575 \cdot 10^{-9} \, \mathrm{m} \).
To determine the photon energy having wavelength \( \lambda = 575 \, \mathrm{nm} \), you use the light quantum hypothesis 1
.
Since the wavelength of the yellow light is given instead of the light frequency, you use the rewritten formula 4
instead of 1
. Thus, the photon energy of the yellow light is:
&~=~ 3.4\cdot10^{-19} \, \mathrm{J} \end{align} $$
In the next lesson, we will use this knowledge about photons to explain a very important experiment in quantum physics, namely the photoelectric effect.
