# Activity: Photoelectric effect

#### Aims

• Understand why the wave model of light fails to explain the photoelectric effect.
• Understand how Milikan measured photoelectron energy.
• Use a simulation to understand the relationship between wavelength and photon KE.
• Explain the photoelectric effect in terms of photons.
• Understand how the Einstein equation represents the photoelectric effect.
• Sketch graphs related to the photoelectric effect.
• Solve problems related to the photoelectric effect.

#### Making predictions

Light is shone on a negatively charged zinc plate. The zinc plate absorbs energy from the EM waves, if enough energy is absorbed then the electrons will be ejected and the zinc plate will lose its charge. Let's use the wave model to make some predictions

If light is a wave it should spread out like ripples in a pond

• What is the difference between a wave with a lot of energy and one with little energy?

• As the ripples spread out what happens to the energy per unit length of wavefront?
• Why does the light from a bulb get dimmer as you move away from it?

Getting an electron out of a zinc plate with light is like getting a ball out of a swimming pool with a water wave. We can use the swimming pool model to predict what will happen in the case of the electron.

This is a good example of how science works, using models to make predictions.(NOS)

Have a look at this animation.

To eject the ball the wave must have a big enough amplitude.

• Does the frequency of the wave affect whether the ball is ejected or not?
• Would a high frequency low amplitude wave eject the ball?

If you made a machine to collect energy from the wave it would be possible to lift the ball out of the pool but there would be a time delay while enough energy was being stored.

Let's now apply this model to the light and electrons.

• According to the wave model what wave property does the brightness of light depend upon?
• Would you expect electrons to be ejected in dim light?
• Would you expect electrons to be ejected in very bright red light?
• Would you expect electrons to be ejected in dim light if it had a high frequency?

These predictions can now be tested by experiment (NOS)

Watch the following video clip

So the predictions were all wrong, does this mean light isn't a wave? What about diffraction and interference?

To explain the experiment we must think about light in a different way, it is still a wave but the wave seems to be in packets or quanta. This is in agreement with the explanation of atomic spectra where light was emitted with specific energy that was related to the change in electron energy level.

#### Quantum model

So how can light be a wave and a particle? That's a difficult one.

Imagine a light bulb placed some distance from a zinc plate. Light spreads out from the bulb in all directions like a wave spreading across a pond. When the light hits the zinc plate an electron is emitted as if it has been hit by a particle. This is all rather difficult to imagine but a simple (incorrect but OK for now) way is to think of light being made of photons.

Light comes in packets (called photons) which behave like particles

The energy of a photon = hf

Light intensity

Intensity is the power per unit area. According to the wave model this should be related to amplitude but in the photon model it would be related to the number of photons.

• Use the photon model to explain why the intensity of light gets less with distance from the source.
• Which colour of light has the most energy per photon, red or blue?
• If you were to compare two equally bright, different colour lights which would have more photons per unit area red or blue?

Explaining the photoelectric effect

Use the photon model to explain why:

• No electrons are emitted with visible light.
• Electrons are emitted with UV light.
• Would electrons be emitted if the UV light was very dim?
• Would electrons be emitted if the visible light was very bright?

If we go back to the swimming pool analogy, what if water waved were quantized?

#### Kinetic energy of photoelectrons

To further verify this model it would be interesting to measure the KE of the photoelectrons, this was done by Milikan in a famous experiment that led to Einstein winning the Nobel prize (he explained the results).

• What do you think the KE of photoelectrons depends upon?

Milikan's experiment

This is a screenshot from the PhET simulation

Light shines on side A and if the frequency is high enough electrons are liberated.

You can see from the orientation of the battery that end B is at a lower potential than A. This means that electrons will be slowed down.

The potential difference between A and B is adjusted until no electrons arrive at B. The max KE of the electrons can then be found.

Try to answer the following questions without the simulation then use it to see if you were right.

• How would you know when no electrons reach B?
• If the stopping potential is 1.5 V what is the maximum KE of photoelectrons?
• What happens if battery is turned round?
• What effect does increasing intensity have on the maximum KE of the electrons?
• What effect does reducing frequency have on the maximum KE of electrons?

The stopping potential is measured for many different frequencies and plotted on a graph (the simulation plots the KE automatically when you vary the frequency but in practice it's not so simple).

• What happens when the frequency is below 0.6 x 1015 Hz ?
• The equation of a straight line is of the form y = Ax + B what do the letters A and B represent?

Einstein explained this graph by saying that the maximum KE is equal to the energy of a photon - the amount of energy required to get the electron out of the metal.

φ is the work function

h is Planck's constant 6.63 x 10-34 Js

• Calculate the work function from the graph shown.
• Calculate Plank's constant from the graph.

Different materials have different work functions so the graph would have a different intercept however the gradient will always be the same.

Threshold frequency (fo)

The threshold frequency is the minimum frequency required for the emission of electrons in a given material. If the frequency of incident light = fo the KE of electrons will be zero so 0 = hfo - φ which implies that φ = hfo

• Calculate the threshold frequency for the previous example.

Other graphs

Exam questions can sometimes be about other features of Milikan's experiment.

This graph compares the current vs potential for the same material and same frequency of light at two different intensities. (try to figure out the answers before using the simulation)

• Which line represents the highest intensity?
• What does the potential V represent and why is it the same at both intensities?
• What effect would increasing the frequency have on the point V?

Exercise 1 to 3 page 285

Photoelectric effect multiple choice quiz

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