The photoelectric effect

Light that frees electrons

Narrated video. Transcript:

In 1887, Heinrich Hertz was making electromagnetic waves with sparks jumping across a gap between two metal knobs. He noticed something strange: the sparks jumped more easily when ultraviolet light from an arc lamp fell on the metal.

The light was helping charged particles escape from the metal surface. Today we call this the photoelectric effect: the emission of electrons from a metal when light of suitable frequency falls on it.

Between 1886 and 1902, Wilhelm Hallwachs and Philipp Lenard studied the effect in detail. Lenard sealed two metal plates inside an evacuated glass tube and joined them to a battery and a meter.

When ultraviolet light fell on one plate, the emitter, a current flowed in the circuit. The moment the light was cut off, the current stopped. Light was knocking particles out of the emitter, and they flew across the vacuum to the other plate, the collector.

Hallwachs put a zinc plate on top of an electroscope and charged it negatively. Watch the leaves when ultraviolet light shines on the zinc: they slowly collapse. The plate is losing its negative charge.

An uncharged zinc plate became positively charged under ultraviolet light. A positively charged plate became even more positive. Every result says the same thing: the light knocks negatively charged particles out of the zinc.

These particles turned out to be electrons. Electrons emitted this way are called photoelectrons, and the current they carry is the photoelectric current.

Then a surprise. If the frequency of the light is below a certain minimum value, no electrons come out at all, however bright the light. This minimum is the threshold frequency, and it is different for different metals.

Zinc, cadmium and magnesium respond only to ultraviolet light, which has a high frequency. Alkali metals like lithium, sodium, potassium, caesium and rubidium respond even to visible light. Such materials are called photosensitive substances.

Intensity and collector potential

Narrated video. Transcript:

Here is the apparatus for studying the photoelectric effect. An evacuated glass tube holds a photosensitive plate C, the emitter, and a metal plate A, the collector. Light enters through a quartz window, because quartz lets ultraviolet light through.

A battery and a potential divider set the potential of A relative to C, and a voltmeter reads it. A microammeter in the circuit measures the photocurrent.

First, keep the frequency of the light and the potential of A fixed, and change only the intensity. Double the intensity, and the photocurrent doubles. The photocurrent is directly proportional to the intensity of the light.

The current tells us how many electrons arrive each second. So the number of photoelectrons emitted per second is proportional to the intensity of the incident light.

Next, fix the frequency and the intensity, and change the potential of A. Make A positive, so it attracts the electrons. As the potential rises, the current grows and then levels off. This maximum is the saturation current: every emitted electron is now collected.

Now make A negative with respect to C. It repels the electrons. Only electrons with enough kinetic energy can push through to A, so the current falls.

At one particular negative potential, the current drops to zero. Even the fastest electrons are turned back. This is the stopping potential, or cut-off potential, V₀.

The retarding field takes away all the kinetic energy of the fastest electron. So K max equals e V₀. A stopping potential of 1.5 volt means K max is 1.5 electron volt, which is 1.5 × 1.6 × 10⁻¹⁹, or 2.4 × 10⁻¹⁹ joule.

Repeat with brighter light of the same frequency. The saturation current is bigger, but the curve reaches zero at exactly the same stopping potential. So the maximum kinetic energy of the photoelectrons does not depend on the intensity of the light.

The effect of frequency

Narrated video. Transcript:

Now keep the intensity fixed and change the frequency of the light. Here are the current–voltage curves for three frequencies, ν₁, ν₂ and ν₃, with ν₃ the highest.

All three curves level off at the same saturation current, because that depends on the intensity. But they reach zero at different places. The higher the frequency, the more negative the stopping potential.

So the maximum kinetic energy of the photoelectrons grows with the frequency of the light. Violet light gives faster electrons than green light; ultraviolet gives faster ones still.

Now plot the stopping potential against the frequency for one metal, say sodium. The points fall on a straight line.

Follow the line down. It meets the frequency axis at ν₀, about 6.6 × 10¹⁴ hertz for sodium. Below this frequency, no electrons come out at all. This is the threshold frequency.

Do the same with another metal, like caesium. We get another straight line, parallel to the first, but meeting the axis at a different threshold frequency. The slope is the same for every metal.

One more observation. Emission starts instantly. Even with very dim light, the current begins within about 10⁻⁹ second of switching the light on. There is no waiting.

So, four facts. The photocurrent is proportional to the intensity. The maximum kinetic energy depends on the frequency, not on the intensity. There is a threshold frequency for each metal. And there is no time lag.

These four facts are a puzzle. In the next lesson we will see that the wave theory of light cannot explain them.

Try it: the photoelectric lab

Interactive simulation. Things to try:

• Move the collector potential V from positive to negative and watch the electrons turn back. Press “Find V₀” to jump to the stopping potential.
• Press “Keep curve”, then double the intensity. The saturation current doubles, but the curve hits zero at the same −V₀.
• Keep the intensity fixed and shorten the wavelength (higher ν). The saturation current stays the same, but V₀ grows.
• Make the wavelength long enough and the electrons stop completely, however bright the lamp. Try caesium and platinum: their thresholds are very different.
• Switch to the V₀–ν graph and record (ν, V₀) at a few wavelengths for two metals. The lines are parallel.

Brighter light

In a photoelectric experiment, the intensity of the light is doubled while its frequency is kept the same. What happens to the saturation current and to the stopping potential?

1. Both double
2. The saturation current doubles; the stopping potential stays the same
3. The saturation current stays the same; the stopping potential doubles
4. Neither changes

Reading the stopping potential

The photocurrent from a metal becomes zero when the collector is at −1.5 V relative to the emitter. What is the maximum kinetic energy of the photoelectrons?

1. 1.5 J
2. 2.4 × 10⁻¹⁹ J
3. 9.4 × 10¹⁸ J
4. 1.5 × 10⁻¹⁹ J

Summary

• Maximum kinetic energy: K_max = ½ m v²_max = e V₀
• Saturation current: I_sat ∝ intensity (fixed ν)
• Threshold: no emission for ν < ν₀

• The photoelectric effect is the emission of electrons from a metal surface when light of suitable frequency falls on it (Hertz, Hallwachs, Lenard).
• The photocurrent, and so the number of photoelectrons per second, is proportional to the intensity.
• The stopping potential V₀ is the retarding potential that just stops the fastest electrons. It does not depend on the intensity.
• V₀ increases linearly with frequency. Below the threshold frequency ν₀ (different for each metal) there is no emission, however bright the light. The V₀–ν lines of different metals are parallel.
• Emission is practically instantaneous (within about 10⁻⁹ s), even for very dim light.