# FHSST Physics/Modern Physics/Wave-particle Duality

Modern Physics The Free High School Science Texts: A Textbook for High School Students Studying Physics Main Page - << Previous Chapter (The Atom) - Next Chapter (Inside the Atomic Nucleus) >> Quantum Introduction - Wave-particle Duality

# The wave-particle duality

Looking at things we can see with our eyes, it seems that wave and particle behavior belong to distinct types of object, but as science reached the atomic and subatomic levels it gradually appeared that each of these is really a property shared by everything. We start by talking about light, but the same concepts apply to everything else, at the atomic scale of size and momentum.

The wave nature of light is demonstrated by diffraction, interference, and polarization of light and the particle nature oflight is demonstrated by the photoelectric effect. So light has both wave-like and particle-like properties, but only shows one or the other, depending on the kind of experiment we perform. A wave-type experiment shows the wave nature, and a particle-type experiment shows particle nature.

How do we know light acts like a wave?

Demonstrating that light has wave properties: imagine dropping a pebble in water - you see circular waves stretching out in ever widening circles. Now imagine placing a barrier (for example a card or piece of wood) in the path of the wave - but a barrier with a slot cut in it. What you would see is the wave hit that barrier and its slot - and a second wave would emenate from the other side of the slot (these would be semicircular waves). This is easy to see at home - try it in a bath of water - well, light waves do the same thing. However, now imagine having not one slot in the barrier, but two. What you would see then is the initial wave hit the barrier - and two semicircular waves emenate from the other side - one from the other side of each slot. The key point is that these two semicircular waves would crash into each other at some point - they would 'interfere' with each other. Where their respective waves were both 'high' they would add up and you would get a peak. Similarly where their respective waves were both low they would add up (you would get an even deeper trough), but where they were in opposite states (one high, one low) they would cancel each other out. If you could stand on the shore with your eye at water level what you would see is a series of peaks and gaps - a sort of stripped imaged. This is exactly what we see when we place a detector (for example a piece of photographic film) on the other side of the two slots when you pass a light wave light through the two slots. You see the stripped pattern where the peaks have left an image (light had fallen on the photo paper) and the gaps (where light had not fallen on the paper) - indicating that 'interference' had taken place - and that indicates that light must be behaving like a wave.

Actually you see a hint of this in supermarkets, when they scan the bar codes with lasers. Ordinary light is a mixture of wavelengths, so that the diffraction patterns of different wavelengths cover each other up. The light from a laser is all the same wavelength, so the random diffraction patterns are visible as speckles.

Now, we consider light to behave not as a wave, but as particles. But what do we call a 'particle' of light?

Photon : A photon is a quantum (energy packet) of light.

Imagine a sheet of metal. On the surface, there are electrons that can be set free. If a photon comes along and strikes the surface of the metal, then it will give its entire energy packet to one electron. This means that the electron now has some energy, and it may escape (leave the surface) if this energy Ek (kinetic energy) is greater than the minimum energy required to free an electron Emin.

Now, suppose the electron needs 5eV of kinetic energy to escape. And suppose this little photon has just 2eV of energy in its energy packet. Then the electron will not leave the surface of the metal. But suppose the photon has 8eV of energy. This means that the electron will emerge with 3eV of kinetic energy.

Note that this does not mean the photon can give 5eV of energy to one electron and 3eV to another. A photon will give all of its energy to just one electron.

The minimum amount of energy needed for an electron to escape (electrons do not normally leave a metal whenever they please), is called the work function of the metal. In our example, the work function is 5eV. The work function has a different value for each metal: 4.70eV for copper and 2.28eV for sodium. It is worth mentioning that the best conductors tend to be those with the smallest work functions. (For Advanced Readers: Work Function actually represents the energy required to overcome the negative potential energy of the electron which is caused by the electrostatic attraction acting on the electron by the nucleus)

The frequency of the radiation is directly related to the energy of the photon. It is important because if the frequency (and hence the energy) of the photon is below a certain threshold value, no electrons will be emitted. Even if the intensity of the light is increased, and the light is allowed to fall on the surface for a long period of time, if the frequency of the radiation is below the threshold frequency, electrons will not be emitted.

The energy of the photon is calculated using the formula: E = hν (where h = 6.57 X 10^-34 J-s is Planck's constant, and ν is the frequency of the radiation).

The kinetic energy of an electron that escapes from the metal is equal to the energy of the photon minus the work function, Φ, i.e.

Ek = (hν) - Φ

The electrons emerge with a range of velocities from zero up to a maximum Vmax. The maximum kinetic energy, (1/2)m(Vmax)^2, depends (linearly) on the frequency of the radiation, and is independent of its intensity.

For incident radiation of a given frequency, the number of electrons emitted per unit time is proportional to the intensity of the radiation.

Electron emission takes place from the instant the light shines on the surface, i.e. there is no detectable time delay.

What are the uses of the photoelectric effect?

The most common use of photoelectric effect is in solar cells. Light energy from the sun is used to excite electrons out of metal surfaces which can then be made to flow in a circuit (i.e., replace a conventional cell!). The current obtained depends on the intensity (or simply: the brightness) of the light.

For this (and other work), Einstein received the Nobel Prize (Physics) in 1921 ("...for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect.").