Introductory physics: the photoelectric effect

One of the last lectures in an introductory physics course is usually a description of the photoelectric effect. This is because the effect is a beautiful manifestation of one of the astonishing discoveries of modern physics; that light, known to behave as an electromagnetic wave, can in some circumstances behave as a stream of discrete particles.

The first hint of this dual nature of light arose from Planck’s study of blackbody radiation in 1900 (see post on radiation). Planck found that he could only predict the observed spectrum of radiation from a hot body if it was assumed that the radiation was transferred between the body and the walls of a container in tiny, discrete packets or quanta of energy, each quantum having an amount of energy given by E = hf ; here f is the frequency of the radiation and h is a fundamental constant of nature (extremely small) that became known as Planck’s constant.

This assumption was regarded as something of a puzzling mathematical trick until a young Einstein suggested in a famous paper that it was the light itself (as opposed to some transfer process) that was quantized i.e. the blackbody spectrum could be described by assuming that light was behaving like a stream of extremely small, discrete bundles of energy, each of energy E = hf. This was a bold assumption as the wave properties of light were well established, but Einstein backed up the idea by showing it explained several other puzzling phenomena, not least the photoelectric effect.

The photoelectric effect was a well-known phenomenon whereby light incident on a metal could cause electrons to be released by the metal (measurable as an electric current). A great puzzle was that the effect ocurred only for light above a certain frequency, characteristic of the metal under investigation; this result was completely inexplicable in terms of the familiar wave theory of light.

Light of a certain frequency incident on a metal causes a current to flow

Einstein showed that the photoelectric effect could be easily explained if the incoming light was behaving as a stream of discrete packets (or photons) of energy. Invoking the conservation of energy, he predicted that the maximum kinetic energy (K.E.) of electrons liberated from the metal would be given by

K.E._e =  hf  –  W₀

where each incoming photon of light has an energy of hf and W₀ is the binding energy (or work function) of the metal. Clearly, electrons could be released from the metal only if the incoming light was of a frequency such that hf  >  W₀ , irrespective of the intensity of the radiation! Could it be that simple? The experimentalist Phillipe Lenard disliked Einstein’s idea intensely and set about disproving it in a series of experiments; years of careful experimentation showed that Einstein’s theory was exactly right in its predictions (see here for more details).

Experimental measurement of the photoelectric effect: no electrons are emitted below the cut-off frequency

The explanation of the photoelectric effect was a significant breakthrough in physics as it represented the first unequivocal evidence of duality; the phenomenon whereby light can behave as a wave in some situations and as a stream of particles (or quanta of energy) in others. This duality formed a cornerstone of the new quantum theory and was later found to be a universal truth of the microworld –  entities known as  ‘particles’ such as electrons and even atoms were in turn found to exhibit wave behaviour.  Indeed, the quantum equation E = hf is as important in modern physics as E = mc² and it was for his explanation for the photoelectric effect (not for special or general relativity) that Einstein was awarded the 1921 Nobel Prize in physics.

Historical note

Philosophers and journalists often claim that ‘Einstein disliked quantum theory’. It should be clear from the above that Einstein was one of the major pioneers of quantum physics; his view of quanta of light was far ahead of its time and was at first strongly resisted by the scientific establishment (including Planck). What Einstein disliked was a later interpretation of quantum theory known as the Copenhagen interpretation, a view of the quantum world that is still debated today.

Excercise

If light of wavelength 780 nm is incident on sodium metal (work function of 3.6 x 10^-19 J), calculate the maximum kinetic energy of emerging electrons. (Hint: recall that wavelength and frequency are related by c = fλ and note that h = 6.6 x 10^-34 Js )