The Photoelectric Effect

At the end of the 19th century the prevailing wisdom was that physics was done and dusted, all solved, nothing more to see or do. Just a few bits and pieces like the ultraviolet catastrophe and the photoelectric effect to sort out and then everyone could go home for some well deserved tea and crumpets while they thought about which of the other natural sciences to muck about in. It wasn't long before a young physicist called Albert came up with a solution to the photoelectric effect's problem (for which he eventually won a Nobel Prize since no one really understood all his other discoveries), and turned physics on it's head with the beginnings of quantum mechanics. Here's how the photoelectric effect experiment proves that light behaved like a particle.

How the experiment works What the results should be - Light is a wave What the results are - ??? Explaining the results - Light is a particle So there we have it...

How the experiment works

From a physics point of view, this is a simple process. Light carries energy. Electrons in a metal absorb the energy from the light shined on it. If they absorb enough energy they will become ionised, breaking free of the metal and moving away from it. It's happening right now to your car.

The photoelectric effect is usually presented as a complete experiment, with reverse voltage circuit to determine the maximum kinetic energy and threshold frequency all wrapped up in a vacuum chamber. We're going to keep it simple. A piece of metal connected to ground so that it doesn't develop a charge as it loses electrons (ground just replaces them immediately), and a source of light where we can change the frequency and the amount of light however we want. As far as we are concerned, all electrons emitted by the metal are detected - through "magic" if you will. This allows us to look at exactly what is going on with just the interaction between light and electrons.

The simplest version of the photoelectric effect.

The experiment is simple, shine light of a given frequency on to the metal plate and record the number of electrons emitted per second over a long period of time (as an addition, we can also measure the maximum kinetic energy of the electrons). Repeat for a range of brightnesses of the light, and repeat the whole thing for different frequencies.

What the results should be - Light is a wave

We know light is a wave, only waves diffract and interfere - and light definitely does that. So, if that's the case (or to put it a better way: Our hypothesis is that "Light is a wave"), what is our prediction?

Before we address that question, we need to look at a key concept - Intensity: the power delivered per unit area. The power comes from two distinct sources, frequency (the colour of the light) and brightness. Increase the frequency and more wavelengths are delivered per second, increase the brightness and the amplitude of the wave increases therefore increasing the energy carried by each wavelength. As far as the metal is concerned, there is no difference between a high frequency with low brightness and a low frequency with high brightness. If the resultant intensity is the same then the average energy transferred to an electron per second should be the same.

So, what does this continious transfer of energy cause to happen?

Imagine a bucket with a hole in it, and a few plastic balls. What happens if you pour water into the bucket?

If you slowly pour water into the bucket the water will simply leak straight out, leaving behind some slightly damp balls. Pouring faster will cause the water level in the bucket to rise as rate of water going in is greater than the rate of water going out. As the water level gets higher, the pressure would increase the rate at which water flows out through the hole, eventually reaching an equilibrium with the balls floating part way up the bucket. If you can pour water into the bucket faster than it can leak out then the bucket will fill up and the balls will go floating off across the floor.

Model of the photoelectric effect using buckets and water.

In case it wasn't clear, the bucket is the atoms, the balls are the electrons, the water is the light energy, and floating off across the floor is ionisation. As with any model, this one has some flaws, but hopefully you get the idea.

When the intensity of the light is low (low frequency and brightness) then nothing happens, at all, ever. The rate of energy loss is greater than the rate energy is provided. As the intensity of the light increases nothing happens, at least until we reach the critical intensity. At the critical intensity (e.g green light and medium brightness, or bright red light, or dim blue light) electrons suddenly start getting released, all be it at a very low rate. Increasing the intensity increases the number of electrons released per second at a roughly linear rate - doubling the amount of energy available per second above the threshold should double the number of electrons released per second.

The word 'suddenly' is perhaps the wrong one. It takes time for the energy level of the electron to build up to the point of ionisation, especially if the intensity is only just above the critical point.

Now, you might be thinking "If it takes ten seconds for an electron to gain enough energy to become ionised, why wouldn't we see bursts of electrons every ten seconds?". Good question. The answer is that even with classical wave theory we expect randomness due to the movement of the electrons. Some will be in the right position to pick up energy quickly, others will take more time. You might be able to detect a trend in the rate of emission if you looked hard enough, but taking an average over even a short period of time would hide that as the replacement electrons also get ionised.

So, our result should only depend on the intensity of the light. We therefore expect the following results:

• There will be a threshold intensity, below which there is no electron emission.
• For a constant frequency, there will be no electron emission below a critical brightness and a slowly increasing emission above it.
• For a constant brightness, there will be no electron emission below a critical frequency and a slowly increasing emission above it.
• The same intensity, whether that's bright red light or dim blue light, will give the same electron emission rate.
• There will be a delay between the light turning on and electrons being emitted.

As an aside, the kinetic energy of the emitted electrons will depend on the intensity of the light since the electrons will continue to absorb energy from the light as they move away from the metal.

What the results are - ???

If we got what we expected then the photoelectric effect would be hardly worth mentioning, let alone a Nobel Prize. Here's what we actually get:

• There is a threshold frequency, below which there is no electron emission.
•   For a frequency below the threshold frequency even very high intensity due to extremely high brightness liberates no electrons*.
•   For a frequency above the threshold frequency even very low intensity due to extremely low brightness liberates electrons.
• For a high brightness, increasing frequency across the threshold produces a step up from no emission to a high rate of emission.
• Above the threshold frequency, increasing the frequency does not increase the rate of electron emission**.
• Above the threshold frequency, increasing the brightness increases the rate of electron emission***.
• There is no delay between the light turning on and electrons being emitted.

* - Not quite true, a few electrons are emitted at very high brightnesses but far fewer than expected.
** - Not quite true, there is a slight increase in emission rate at very high frequencies, but not by much. It does increase the maximum kinetic energy of the electrons though.
*** - It does not increase the maximum kinetic energy of the electrons, with the exception of a very very small number of electrons.


That's about as far away from the expected results as you can get without something ridiculous happening, like the metal turning into a duck. The light can't be a wave, so what is it?

Explaining the results - Light is a particle

Thinking of the light as being made up of particles requires not just a change in the behaviour of the light, but also of the atom.

The fundamental difference between light as a wave and light as a particle if how the energy it transfers is delivered. As we've discussed above, a wave delivers energy continiously over time; a particle, however, delivers its energy all at once. Since the electrons lose energy by emitting light, they must lose it all at once (or at least in large chunks) too.

Coming back to our bucket analogy, this bucket doesn't have holes in it but a 'helpful' person keeps emptying the water out for you. You aren't pouring the water in anymore, you're emptying a container of water in instead. So, if you put half a bucket of water in at a time then by the time come back with a second half a bucket of water the bucket will have been emptied and the balls will stay in the bottom. If you can add enough water in one go then the balls will float off before the water is removed.

Model of the photoelectric effect using buckets and water - take 2.

As with waves, the intensity of the light is determined by the frequency and the brightness - but now they mean something different. The frequency is a measure of the energy that an individual particle of light has, all particles with the same frequency carry the same energy. The brightness is the number of particles per second. So, if you want to double the intensity you can double the energy carried by each particle (double the frequency) or double the number of particles (double the brightness).

The photoelectric effect using particles of light.

The Photon - these particles of light were given a name, photons. It makes it easier to talk about them.

So, does that explain our experimental results? Let's have a look:

• There is a threshold frequency - If a photon has enough energy to cause ionisation then it will, if it doesn't then it won't.
• Photons below the threshold frequency ionise no electrons - The average time between photon absorptions is far longer than the average time between absorption and re-emission, unless the brightness is very high. This means that the double absorption necessary to cause ionisation is a very rare event.
• A very dim source of high frequency photons causes ionisations - A single photon above the threshold frequency causes an ionisation if it is absorbed.
• A bright source produces a sudden burst of electrons when the threshold frequency is reached - Lots of sub-threshold photons will ionise no electrons, lots of threshold+ photons will ionise lots of electrons, leading to a step-up in the number of electrons ionised.
• Increasing the frequency does not increase the number of ionisations - A photon can only deliver its energy to one electron, therefore a higher frequency does not lead to more electrons, only to electrons with greater kinetic energies. If the frequency is very high then instead of being absorbed the photon is scattered, transferring enough energy to cause ionisation as it bounces off. The scattered photon may retain enough energy to cause a second (etc) ionisation. This is noticable is gamma rays are used.
• Increasing the brightness increases the number of ionisations - Doubling the number of photons doubles the number of interactions, and therefore the number of ionisations. Since the electrons can only gain more energy by double photon absorption their KE does not increase. While double absorption is possible, it must take place near a charged particle in order to conserve energy and momentum. Since the electrons are leaving the material, that would be a much rarer event than the already rare double absorption of sub-threshold photons.
• Ionisation is instantaneous - As soon as a photon reaches the metal from the light an electron is ionised, even if the intensity is very low (the required energy is transferred all at once, not over time).

So there we have it...

Light is made up of particles, that we call photons. Photons give us theoretical results that exactly match what we get from experiments, while waves cannot match any of the observations.

But experiments involving diffraction and interference give the opposite result. So what is light?

The answer is both simple and complex. Simply, the answer is neither, in the same way that a plane isn't bird or a bus. If you had no concept of what a plane was and saw it flying through the sky, you'd think it was bird. Similarly, if you saw people getting into it and it driving off down the runway, you'd think it was a bus. Mostly we say that photons have wave and particle like properties, use the term wave-particle duality, and get on with our day. The complex answer is the mathematical description given by quantum mechanics, that (so far at least) explains the behaviour of light in all circumstances (except near a black hole where current physics doesn't work very well - not that we have a way of testing our models at the moment).

An impression of what photons might be like.