doPhysics · Modern Physics
Photons and the Photoelectric Effect
Light that frees electrons from a metal. The work function and the electron volt, the photocell and its four facts, the failure of the wave picture, Einstein's photon and his equation, the photoelectric graphs, the photon's energy and momentum, and the pressure of light.
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Why this chapter
Why this chapter exists
Light shining on a metal can knock electrons out of it. Around 1900 this looked like a small puzzle in a glass tube. It turned out to be the crack through which the whole of modern physics came in. The wave picture of light, which explained interference perfectly, could not explain which colours free electrons or how fast they fly. Einstein's answer was that light arrives in packets, photons, each with an energy set by its colour. This chapter follows the experiment to that answer. It ends with the photon as a particle with energy and momentum, strong enough to push a comet's tail and a spacecraft.
You will learn
By the end of this chapter you will
- Say what the work function of a metal is, and convert energies between joules and electron volts.
- Describe the photocell circuit, and state its four facts: current and intensity, saturation, the stopping potential and the threshold frequency.
- Explain why the wave picture of light fails on intensity, threshold and time, and how photons succeed.
- Use Einstein's equation \(K_{max} = h\nu - \phi = eV_0\) to find stopping potentials, threshold frequencies and wavelengths, and work functions.
- Read the graphs of \(V_0\) against \(\nu\) and of current against collector potential, and find Planck's constant from a slope.
- Find the energy, momentum and number per second of the photons of a source.
- Find the force of light on black, mirror and partly reflecting surfaces, at normal and at oblique incidence.
Before you begin
Before you begin
From the chapter on Work, Kinetic Energy and Power, you should know kinetic energy \(\tfrac12 mv^2\) and the work-energy theorem. From Newton's laws you should know that force is the rate of change of momentum. From the chapters on waves you should know \(c = \nu\lambda\), and that the intensity of a small source falls as \(1/r^2\). Each fact about electric charge and potential that the chapter needs is stated where it is first used.
Lessons
1
Light That Frees Electrons
Electrons move freely inside a metal but are held back at its surface. The least energy that frees one is the work function, measured in electron volts. Heat, a strong electric field or light can supply it.
Electron emission and the work functionThe electron voltThree ways to free an electron
2
The Photocell and What It Shows
An evacuated tube with an emitter, a collector and a microammeter turns freed electrons into a current. Four facts come out of it - the current follows the intensity, it saturates, a stopping potential measures the fastest electron, and below a threshold frequency nothing happens at all.
The photocell circuitCurrent against intensitySaturation current and stopping potentialThreshold frequency and no time lag
3
Why Waves Fail and Photons Succeed
A wave spreads its energy smoothly, so it predicts faster electrons in brighter light, no threshold and a long wait in dim light. All three are wrong. Einstein's photon, a packet of energy \(h\nu\) given whole to one electron, explains every fact with one equation.
Three predictions of the wave theoryEinsteins photon hypothesisEinsteins photoelectric equation
4
Reading the Photoelectric Graphs
The stopping potential against the frequency is a straight line of slope h/e for every metal, starting at the metal's threshold. The current against the collector potential shows intensity in its height and frequency in its stopping potential. Millikan read Planck's constant from the slope.
Stopping potential against frequencyCurrent against anode potentialPlanck constant from the slope
5
The Photon as a Particle
A photon moves at \(c\), has no rest mass, and carries energy \(hc/\lambda\) and momentum \(h/\lambda\). Dividing a source's power by one photon's energy counts its photons, and intensity turns out to be a count of photons, not their size.
Photon energy and momentumPhoton flux of a sourceIntensity counts photons
6
Light Pushes: Radiation Pressure
Photons carry momentum, so a surface that absorbs or reflects light is pushed. A black surface feels P/c and a mirror 2P/c at normal incidence. At an angle only the normal part of the momentum reverses, and a partly reflecting surface lies in between.
Force of light on an absorber and a mirrorRadiation force at oblique incidencePartly reflecting surfaces
Read in order. The small labels are the topics of each lesson. They take your colour as you answer the checks.
0%The Workbook
Questions to solve on paper, marked by you.
Glossary
The key words of this chapter, with the meaning this chapter gives them.
- electron volt
- The energy an electron gains in crossing a potential difference of one volt, \(1\,\text{eV} = 1.6 \times 10^{-19}\,\text{J}\). A unit of energy, not of potential.
- field emission
- The escape of electrons from a cold metal pulled out by a very strong electric field, usually at a sharp tip.
- photocell
- An evacuated tube in which light frees electrons from an emitter and a collector gathers them, so that light produces a current.
- photocurrent
- The current in a photocell circuit, carried by photoelectrons that reach the collector. A current \(I\) means \(I/e\) electrons each second.
- photoelectric effect
- The emission of electrons from a metal surface when light of a suitable frequency falls on it.
- photoelectric emission
- The escape of electrons from a metal when light supplies the energy.
- photoelectron
- An electron freed from a metal by light.
- photon
- A packet of light energy. A photon of frequency \(\nu\) carries energy \(h\nu\) and momentum \(h/\lambda\), moves at \(c\), and is absorbed whole by one electron.
- Planck's constant
- The constant of nature that sets the size of a photon, \(E = h\nu\), with \(h = 6.63 \times 10^{-34}\,\text{J s}\).
- quantum efficiency
- The fraction of the photons falling on a surface that free an electron. It is often a few per cent.
- radiation pressure
- The force per unit area that light exerts on a surface it strikes. At normal incidence it is \(I/c\) on a black surface and \(2I/c\) on a mirror.
- reflectivity
- The fraction \(r\) of the light falling on a surface that it reflects; the rest, \(1 - r\), is absorbed.
- rest mass
- The mass of a body measured when it is at rest. A photon is never at rest, and its rest mass is zero.
- saturation current
- The largest photocurrent for a given light, reached when the collector is positive enough to gather every freed electron. It is proportional to the number of photons arriving each second.
- stopping potential
- The least retarding potential of the collector, relative to the emitter, that makes the photocurrent zero, written \(V_0\). It measures the fastest electron: \(K_{max} = eV_0\).
- thermionic emission
- The escape of electrons from a heated metal, when heat gives a few of them more than the work function. A hot filament emits this way.
- threshold frequency
- The least frequency of light that frees electrons from a given metal, \(\nu_0 = \phi/h\). Below it there is no emission at any intensity.
- threshold wavelength
- The longest wavelength of light that frees electrons from a given metal, \(\lambda_0 = hc/\phi\); in nanometres, \(1240/\phi\) with \(\phi\) in eV.
- work function
- The least energy that must be given to an electron to remove it from the surface of a metal, written \(\phi\). It is a few electron volts: \(2.14\,\text{eV}\) for caesium, \(4.65\,\text{eV}\) for copper.