Photoelectric effect and the dual nature of light As we said before, the 1805 double-slit experiments in which Thomas Young observed distinct interference effects wielded a “mortal blow” to Newton’s theory that described light as a stream of tiny ‘light particles”. The following years were marked by many new triumphs of the wave theory of light. A real milestone event was the theory of James C. Maxwell ( ) that led to the prediction that light is an electromagnetic wave.

But still missing was an experimental proof that EM waves can be generated by electric circuits, as was also predicted by the Maxwell theory. A series of crucial experiments that validated Maxwell’s theory was carried out by a German physicist Heinrich Hertz in His results were acce- pted as the final proof for the electro- magnetic nature of light waves. But Mother Nature is mischievous… Heinrich Hertz ( )

Because in the very same year of 1887, the very same person, Hertz, discovered another surprising effect induced by light: namely, that light incident on metal surfaces knocks out negative electric charge from them! This phenomenon was named the Photoelectric Effect. In 1887 it was not known that the carriers of negative charge are tiny particles – the electrons. They were discovered only ten years later, in 1897, by a famous British physicist, J.J. Thomson (who is perhaps better known as Lord Kelvin). J. J. Thomson (Lord Kelvin)

Soon it was unders- tood and confirmed by new experiments that in the photoele- ctric effect light knocks out electrons from the metal. Was it a simple explanation? Not really… It caused a lot of embarrassment among physicists because… the experimental findings seemed to be in clear contradiction with the wave nature of light!

It’s natural to expect that it is the electric field of the EM wave that rips out the electrons from the metal. Light of lower frequency (red): Light of higher frequency (blue): Lower light Intensity: Higher light Intensity: The maximum electric field value depends on the intensity, but not on the frequency.

1.Expected, based on the wave theory: Increasing light intensity  increasing kinetic energy of the electrons knocked out. Observed: Increasing the intensity of the light increases the number of photoelectrons, but not their maximum kinetic energy! So, what can be expected? – and how do the expectations agree with the observations?

2. Wave theory, expected: it’s the electric field of the EM wave that “pulls out” the electrons from the metal. The strength of the wave’s electric field depends on it’s intensity, but not frequency. Then, lights of all colors should produce similar effects. Observed: Red light does not cause the ejection of electrons, no matter what the intensity! Observed: Green light does eject electrons, but their kinetic energy…. …is lower than of those ejected by violet light!

Let’s summarize, in a graphic form:

At the beginning of the XX century, the peculiar behavior of photoelectrons was thought of as one of the “major unsolved mysteries” in physics. It was young Albert Einstein who found a solution of this riddle. In 1905, he showed that one can fully explain the photoelectric effect by assum- ing that light is actually made up of lots of small “packets” of energy called photons that behave like particles.

According to Einstein, the energy carried by an individual photon depends only on its frequency ν – namely, as: where is a constant known as the “Planck Constant”. In the photoelectric effect, the photon disapp- ears, and all its energy acquired by the photo- electron in the form of kinetic energy K :

It already explains two facts: 1.Light intensity increases  number of photons increases  number of photoelectrons incre- ases (but not their kinetic energy!). 2. Light frequency increases  photon energy increases  photoelectron energy increases. Still, it does not answer the question why red light does not produce photoelectrons!

In order to explain the latter fact, we need to say something about electrons in metals: They can be thought of as sort of an “electron fluid” (actually, the official term is “Fermi fluid of mobile electrons”). There is much analogy between this fluid, and water in a glass not filled up to the rim.

The potential energy of the “topmost” electrons is lower than that of electrons outside (i.e., of free electrons) by W. Therefore, a portion of energy equal W is ne- eded to pull the electr- on out of the metal. By tradition, W is called the “Work Function”

In view of the above, taking into account the energy conservation, we can conclude that the kinetic energy of a photoelectron getting out of the metal is: This is the famous Einstein’s formula, for which he was awarded a Nobel Prize in 1921

Small digression: energy units The energy unit in the SI system is a Joule (J): However, the energies of photons expressed in Joules would be very small numbers. Therefore, for the sake of convenience, we use a much smaller unit called “electron-Volt” (eV):

Digression (2): Planck Constant in terms of eV: The photon energy is E=hν. But the frequency ν of visible light is a very large number, which also makes it inconvenient; a more “user-friendly” is the wavelength :

Digression (3): Examples: [nm] E ph [eV]

Back to photoelectric effect: Example: PE in Potassium metal: Potassium: W = 2.0 eV

Here is another instructive picture (T max in this graph has the same meaning as K in the other slides, and V(z) is the potential energy).

The values of work function W for various metals (note that Cesium (Cs) has a record-low work function value).

In 1905, Einstein’s theory of PE based on “light particles” (photons) was so revolutionary that it was met with wide scepticism. However, in the following years much new experimental evidence supporting the theory was obtained, and the scepticism gradually changed to a wide acceptance. Did Einstein’s theory “wipe out” the wave theory? No, the wave theory is still in good health! How comes? Well, we have to accept that light has a “dual nature”: in some phenomena it behaves like a wave, and in some others, like a beam of particles.

Discussion of the dual nature of light in greater detail goes beyond the scope of this course – however, I encourage all of you to learn more for your own “intellectual profit”. There is a lot of material on this subject on the Web.

PRACTICAL EXAMPLE: In an experiment with a metal sample, it was found that light of wavelength 420 nm ejects photoelectrons of energy 0.65 eV from its surface, and light of wave- length 310 nm ejects electrons of energy 1.69 eV. Find the value of the work function of this metal – show that you don’t need to know the Planck constant value to solve the problem.