# The Photoelectric Effect

by Jared Rovny

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00:01 So this finishes up almost with one last topic.

00:04 Sorry, the Photoelectric Effect.

00:07 This photoelectric effect is really, really interesting historically.

00:12 So, one title for this possible section could be how to get a noble prize.

00:16 Because would happened historically is that they saw an effect that they did not understand until Einstein came along and developed a theory about how particles could be quantized.

00:26 And this in fact what he got his noble prize for.

00:28 So let's explore this effect a little bit.

00:31 What they noticed starting with this idea that we already introduced, is that you could send light and if you hit an atom with a certain energy of light, you could knock the electron free that atom entirely.

00:42 But on the other hand they setup these experiments and this is where the great mystery came in.

00:46 They setup an experiment with a circuit as you see here.

00:50 Where you have some battery.

00:51 They can measure the current through the circuit using an ammeter which we discussed in our circuits chapter.

00:56 And then at the top of the circuit they put these plates with a battery connected to these plates we sort of built up some charge on the two plates.

01:04 So that you have a different charge across the two.

01:08 So the current really wants to flow across these plates but it can't because they are separated by some distance.

01:13 So no current can actually flow.

01:16 On the other hand, if you shine a light on the plates, what can happen is the protons will release the electrons.

01:21 They will knock the electrons off of one plate and the electrons can flow through your circuit.

01:26 You can tell this is happening by just looking at your ammeter.

01:28 The ammeter measuring the current in your circuit.

01:30 So if you see the ammeter jump and go up, you know that current is coming through your circuit.

01:35 The really strange mystery is that when they sent red light to these plates to try to knock the electrons loose so they could flow through the circuit, nothing happened and no current flowed through the circuit.

01:47 On the other hand if they sent higher energy, the blue light through the circuit, the electrons would flow and they would see the current going up.

01:55 But the very strange aspect as you can see represented in this picture was that when they sent in a lot of red light, very high amounts of energy of red, they still did not get the electrons to flow through the circuit.

02:07 And then when they sent in very low energies of the blue light, very flow photons and very small amounts of light, the energy would flow anyways.

02:15 Even though there is very little energy there.

02:17 So this couldn't be described by the classical wave idea of light that was being held and debated the particle idea of light before this point.

02:26 Because if you think of wave, we could send a wave like this one.

02:29 And we could give that wave a very, very high amplitude.

02:32 So you can see we've drawn this wave without high amplitude.

02:34 Meaning that this would be a very energetic wave of light.

02:37 But this very energetic wave of light still didn't managed to get the electron to leave the atom.

02:43 So we needed some new theory to describe why very high energy light couldn't release electrons.

02:48 When seemingly very low energy light could release electrons.

02:52 And this was Einstein's theory.

02:54 And again he received a noble prize for describing and understanding how we could quantize this light instead of being one big wave with a high amplitude as being very many in number, very many low energy red photons of light.

03:09 What this does for us, the way it describes this effect is that as these photons of light come into the atom, the electron will assess each photon individually.

03:20 So as the photons come in, it will look at a red photon of light which again is a low energy photon.

03:26 It will see that this is not enough energy.

03:28 And that photon will leave and the next on will come in.

03:31 In other words a given photon, a given packet of light to have enough energy to release the electron.

03:37 And even if you build up a high amplitude of your light, the high energy just by adding up many, many photons together, you still can't cheat this effect.

03:46 The electron still requires that a particular photon of light have enough energy to knock it away from it's orbital.

03:52 On the other hand, if we send in more of these it will still be too weak.

03:57 Or on the other hand, with the blue light or the higher frequencies, the purple or violet frequencies, even with very low energies of light.

04:05 So just one photon for example, the electron in the atom will assess that photon when it comes in.

04:11 Say yes, this photon has plenty of energy for me to leave my orbital and so the electron will be knocked off the orbital of the atom.

04:19 Even again for very low energies of light.

04:21 So this is called the "Photoelectric Effect." Because the photoelectric circuit that was originally setup to explore this phenomenon showed again that you could send electrons across you circuit with very few higher energy, blue photons and still could not send the current through a photoelectric circuit.

04:38 With a big amount of energy, many, many red photons, each photon which was of a low energy.

04:46 So now we have a last idea which is, What if I sent in an electron out of my atom by hitting it with a photon of light? The question is, How much energy do we need? We just discussed that an electron requires that a particular photon when it comes in, has enough energy to knock the electron out of the atom.

05:05 So asking ourselves how much energy does this needs to be.

05:07 We call this energy the "Work Function." And it is represented by the Greek letter V for a particular atom or a particular electron in an orbital of the atom.

05:17 So we send in a photon, and we already know we remember that we've already learned that the energy of a photon is equal to h Planck's constant times the frequency of that photon.

05:28 So this means if I send a photon with a particular energy and it's released from the atom, it is now leaving and moving away and has some sort of a kinetic energy.

05:37 So the energy of the photon is the only thing that gave the electrons energy to move.

05:42 So this means that the photons energy, when it hits the electron partly will go into get in the electron out of the atom just releasing it, or freeing the electron from the atom.

05:52 While the rest of the energy is able to go into the kinetic energy of the atom.

05:56 So we can write an equation like this which is really just a conversation of energy equation which says, that on the left hand side the energy of the photon h times f is equal to the two different places that that energy is going.

06:10 Some of the energy will go into the kinetic energy of the photon and some of the energy had to be used to free the electrons from the atom.

06:17 And again that's equal to the work function for a particular atom.

06:21 We can rearrange this equation and find the velocity that the electron will have after it leaves the atom.

06:28 So just be rearranging we put the K, the kinetic energy term on one side of the equation.

06:32 We put the work function V on the other side of the equation.

06:35 And we can write what we know we already about the kinetic energy expression which is 1/2 m v2 square.

06:42 So now we know that 1/2 m v2 square, the kinetic energy of your electron after it leaves the atom has to be equal to the photons energy whatever the original energy that came in, minus how much energy had to used just to free the electron.

06:57 And so we have an expression here for exactly how fast an electron will be leaving an atom if we know both, the energy of the photon that we are sending in and the work function for a particular atom.

07:07 And these work functions are calculated experimentally.

07:09 So there are big tables of these work functions for different kinds of materials.

07:13 So just by knowing light you are sending in, what color of light, what frequency, you can know exactly how fast you are freeing your electrons which is very useful experimentally.

07:23 So this completes our discussion of the electronic structure of atoms.

07:27 We started with the Bohr model and the basic structure of how atoms work in our new model of things.

07:31 We discussed the different shapes that the electrons can take as their orbit an atom.

07:36 The different orbitals as well the different quantum numbers and how they relate to the periodic table.

07:40 And then finally we wrapped it with the discussion of a few more advance concepts in the specifics of how this electronic structure behaves in a few very important experiments.

07:50 Next we'll be going on to some thermodynamics which will be our last topic for this lecture series.

07:55 And until then, thanks for listening.

The lecture The Photoelectric Effect by Jared Rovny is from the course Electronic Structure.

### Included Quiz Questions

1. Electrons were able to be released from a material only when a more blue light was shone, regardless of the total energy.
2. Electrons were able to be released from a material only when a more red light was shone regardless of the total energy.
3. Electrons were able to be released from a material only when a more blue light was shone if the total energy was high enough.
4. Electrons were able to be released from a material only when a more red light was shone, if the total energy was high enough.
5. Electrons were able to be released from a material only when red and blue light were shone on a material together.
1. The red light impinged as individual photons, each of which had too little energy.
2. Red light does not correspond to the proper atomic size for conducting atoms.
3. The uncertainty principle shows that more red light cannot be used to effect electron orbitals.
4. The frequency of red light is too high to release electrons.
5. Light towards the red end of the spectrum can only be contained in fewer photons.
1. The energy required to release an electron from an atom.
2. The function is describing how much work an atom does when emitting light.
3. The work done to move an electron enough to release a photon.
4. The function of energy which describes the type of photon released.
5. The energy of an electron’s lowest orbital in an atom.
1. √(2 (hf - ϕ) / m)
2. hf - ϕ
3. K + ϕ
4. (2 [(hf - ϕ) / m)]^2
5. 1/2 (mv^2)

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