Hello, and welcome back to MPC! Last week, we started to talk about the photoelectric effect. Today, we will resume our discussion and learn about the implications of this intriguing phenomenon.

As a reminder, the photoelectric effect is a phenomenon in which the presence of light causes electrons to be emitted from a piece of metal:

Figure 1: The photoelectric effect

**Note: The emitted electrons are also called photoelectrons.**

Using the classical wave model of light, we determined the following:

Increasing the intensity (brightness) of the light should increase the speed of the emitted electrons .

Increasing the frequency ( color ) of the light should increase the number of electrons emitted from the metal in a given period of time.

However, according to experimentation:

Increasing the frequency ( color ) of the light increases the speed of the emitted electrons.

Increasing the intensity (brightness) of the light increases the number of electrons emitted from the metal in a given period of time.

How can we explain this? Albert Einstein had an idea: what if light is made up of particles?

Einstein’s idea might sound a little odd. Recall from a few weeks ago that Isaac Newton originally predicted that light is made up of particles, but his ideas were disregarded after experiments demonstrating the wave nature of light were conducted (see this post). Nonetheless, Einstein had faith in Isaac Newton and was confident that the photoelectric effect demonstrated the particle nature of light.

The “particle nature of light” is the idea that light consists of particles, called photons, that are moving around in space:

Figure 2: The particle nature of light (photons)

For our purposes, we can picture the photoelectric effect from a “photon perspective” where photons are actually knocking into electrons and bumping them off of the metal:

Figure 3: The “photon perspective” of the photoelectric effect

**Note: Notice that the electrons that are getting hit by photons are the ones that are getting knocked off of the metal.**

Let’s start off by trying to explain (with the photon model) why increasing frequency should increase the speed of the emitted electrons. We know that each photon has a certain amount of energy, and knocking a single electron off of the metal requires a certain amount of energy. Imagine that a photon that does not have enough energy to knock an electron off of the metal hits an electron. What will happen?:

Figure 4: Photons that do not have enough energy to knock electrons off of the metal

**Note: The electron that is getting hit by the “weak” photon will not fly off of the metal. It may be helpful to imagine (for our purposes) the photon simply bouncing off of the electron, with the electron staying in place.**

The electron will not budge! On the other hand, if a photon that has enough energy were to hit an electron, the electron would fly off of the metal!:

Figure 5: Photons that do have enough energy to knock electrons off of the metal

Now, what determines the energy of a photon? In the 20th century, physicists predicted that the energy of a photon is related to the photon’s frequency (not amplitude). Recall that, in terms of visible light, violet has the highest frequency, followed by blue, followed by green, and so on (reverse “rainbow order”).

Figure 6: The electromagnetic spectrum

Believe it or not, the idea that energy and frequency are related conforms perfectly to the photoelectric effect. Scientists found that, when they used higher frequency light, the electrons emitted from the metal would fly off of the metal with a greater speed than those emitted from the metal when lower frequency light was used. For instance, electrons emitted from the metal when violet light was used would fly off of the metal at greater speeds than those emitted from the metal when blue light was used.

Figure 7: The effects of different colors of light on the emitted electrons

**Note: The speed of the emitted electrons is indicated by the length of the arrows.**

The reason for this difference in speed is that violet light, with its higher frequency, has more energy than blue light and can therefore “give” more energy to the electrons.

Another interesting discovery that scientists made is that, below a certain frequency, some light has too little energy to knock any electrons off of the metal! As a hypothetical example, it is possible that no electrons will be emitted from a piece of metal when red light is shining on it, no matter how bright that red light is!:

Figure 8: Below a certain frequency, light does not have enough energy to knock electrons off of the metal

Using the photon model, this strange phenomenon can be explained rather simply: red light has such a low frequency that (in our example) it does not have enough energy to knock electrons off of the metal (see Figure 4). The minimum frequency of light needed for the metal to emit electrons is known as the threshold frequency.

Now, onto intensity! In the wave model of light, the intensity (brightness) of light corresponds to the amplitude of the light. The problem with photons is that they do not necessarily have amplitudes (they are particles, so they do not have crests/troughs like waves do). In the case of photons, the analog to amplitude is the “number of photons.” That is, having a few photons corresponds to dim light while having a lot of photons corresponds to bright light:

Figure 9: The intensity of light in the photon model

(image sources: https://cdn.sparkfun.com//assets/parts/3/6/3/00533-LED_Light.jpg, https://cdn.sparkfun.com//assets/parts/3/5/9/00528-LED_Light.jpg)

So, why does increasing the intensity of light increase the number of electrons that the metal emits? To put it simply, brighter (more intense) light has more photons, meaning that more electrons in the metal will get hit (knocked away) by photons when brighter light is used. Therefore, as long as these photons have enough energy to knock an electron off of the metal, more electrons will be emitted from the metal when brighter light is used than when dimmer light is used:

Figure 10: The effects of different brightnesses on the emitted electrons

In conclusion, Einstein’s photon theory does an excellent job at explaining the photoelectric effect. However, we still have some unanswered questions. For instance, the double-slit experiment still suggests that light is a wave (we cannot use the photon model to describe it). So, is light a wave or a particle? Indeed, it seems like we are back to where we initially started! In next week’s post, though, we’ll come to a “final” conclusion on the nature of light. See you then!

For more information (and a head start on future posts), be sure to check out these resources: https://www.youtube.com/watch?v=U2LJ1oSO8u4, https://www.youtube.com/watch?v=MFPKwu5vugg, https://www.khanacademy.org/science/physics/quantum-physics/photons/a/photoelectric-effect, https://www.scienceabc.com/pure-sciences/what-explain-photoelectric-effect-einstein-definition-exmaple-applications-threshold-frequency.html

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