Photoelectric effect and the dualnature of light

As we said before, the 1805 double-slit experiments in which Thomas Young observed distinct interferenceeffects wielded a “mortal blow” to Newton’s theory thatdescribed light as a stream of tiny ‘light particles”.

The following years were marked by many new triumphsof the wave theory of light. A real milestone event wasthe theory of James C. Maxwell (1861-62) that led to the prediction that light is an electromagnetic wave.

But still missing was an experimental proof thatEM waves can be generated by electric circuits,as was also predicted by the Maxwell theory.

A series of crucial experiments thatvalidated Maxwell’s theory was carriedout by a German physicist Heinrich Hertz in 1887. His results were acce-pted as the final proof for the electro-magnetic nature of light waves.

But Mother Nature is mischievous…

Heinrich Hertz (1857-1894)

Because in the very same year of 1887, the verysame person, Hertz, discovered another surprising effect induced by light: namely, that light incidenton metal surfaces knocks out negative electriccharge from them! This phenomenon was named the Photoelectric Effect.

In 1887 it was not known that the carriersof negative charge are tiny particles – theelectrons. They were discovered only tenyears later, in 1897, by a famous Britishphysicist, J.J. Thomson (who is perhapsbetter known as Lord Kelvin). J. J. Thomson

(Lord Kelvin)

Soon it was unders-tood and confirmedby new experimentsthat in the photoele-ctric effect light knocksout electrons from the metal.

Was it a simple explanation? Not really… It causeda 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 wavethat rips out the electrons from the metal.

Light of lower frequency (red): Light of higher frequency (blue):

Lower lightIntensity:

Higher lightIntensity:

The maximum electric field value depends onthe 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 theexpectations 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 peculiarbehavior of photoelectrons was thought of as

one of the “major unsolved mysteries” in physics.

It was young Albert Einsteinwho found a solution of thisriddle. In 1905, he showed that one can fully explain thephotoelectric effect by assum-ing that light is actually madeup of lots of small “packets”of energy called photons thatbehave like particles.

According to Einstein, the energy carried byan individual photon depends only on itsfrequency ν – namely, as:

where is a constant knownas 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 :

hEphoton

sJ 10626.6 34 h

hKmetal in the

ronphotoelect

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 thequestion why red light doesnot produce photoelectrons!

In order to explain the latter fact, we need to saysomething about electrons in metals:

They can be thought of as sort of an “electron fluid”(actually, the official term is “Fermi fluid of mobileelectrons”).

There is much analogybetween this fluid, andwater in a glass not filled up to the rim.

The potential energy ofthe “topmost” electronsis lower than that ofelectrons outside (i.e.,of free electrons) by W .

Therefore, a portion ofenergy 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 thatthe kinetic energy of a photoelectron gettingout of the metal is:

function work

energy photon

ronphotoelect WhK

This is the famous Einstein’s formula, for whichhe 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 inJoules would be very small numbers. Therefore,for the sake of convenience, we use a much smaller unit called “electron-Volt” (eV):

2

2

s

mkg1J 1

J 101.602 eV 1 -19

seV 10136.4 15 h

Digression (2): Planck Constant in terms of eV:

The photon energy is E=hν . But the frequency νof visible light is a very large number, which also makes it inconvenient; a more “user-friendly” isthe wavelength :

nmeV 1240m10eV 1240

m/s103 seV10136.4

9

815

photon

chhE

Digression (3): Examples:

eV nmin

1240photon

E

[nm] Eph [eV]

700 1.77

550 2.25

400 3.10

Back to photoelectric effect:

Example: PE in Potassium metal:

Potassium: W = 2.0 eV

WEK ph.electr.

Here is another instructive picture(Tmax in this graphhas the same meaning as K in the other slides, and V(z) is thepotential energy).

The values of work function Wfor various metals (note thatCesium (Cs) has a record-lowwork function value).

In 1905, Einstein’s theory of PE based on “lightparticles” (photons) was so revolutionary thatit was met with wide scepticism. However, inthe following years much new experimental evidence supporting the theory was obtained,and the scepticism gradually changed to awide acceptance.

Did Einstein’s theory “wipe out” the wave theory?No, the wave theory is still in good health! Howcomes? 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 ofparticles.

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

PRACTICAL EXAMPLE:

In an experiment with a metal sample, it was foundthat light of wavelength 420 nm ejects photoelectronsof 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 Planckconstant value to solve the problem.