Towards a Quantum Theory of Light

Recap of the theory of lightHistorically, physicists have grappled with

the nature of light as either a stream of particles or a wave phenomenon.

The ray(particle) model of light (i.e light travels in straight lines) was supported by evidence such as shadows cast by the sun and flashlights shining straight beams of light. Furthermore, this theory was supported by Newton and others. It successfully described the properties of reflection and refraction .

Recap of the theory of lightChristiaan Huygens, a Dutch physicist , and a

contemporary of Newton proposed a different theory. He believed that light travelled as waves and that the wave theory could successfully explain the phenomenon of diffraction, the property of waves such as water waves where the waves bend in behind obstacles. Francesco Grimaldi demonstrated that light exhibited the property of diffraction.

If you hold your finger up to a light source and bring it closer to your eye, you will notice that the border of your finger is not clear, but blurry. This suggests that the light waves are bending to get around your finger.

Recap of the theory of lightIn 1801, Thomas Young, a British physicist

conducted his now famous double-slit experiment

Recap of the theory of lightYoung observed the property of light wave

interference. The particle model could not explain these results and the wave theory of light was adopted.

The universal wave equation was given by v = fλ where v = wave speed in m/s , f was frequency in Hz, and λ was wavelength in m

Recap of the theory of lightElectromagnetic waves travelled at the speed

of light i.e. c= 3.00 x 108 m/s and c = fλJames Clerk Maxwell showed that an

accelerating charge generated electromagnetic (EM) radiation i.e. light. Accelerating charges generate an oscillating magnetic field, which in turn generates an oscillating electric field and these travel simultaneously as an EM wave.

Recap of the theory of lightAll forms of electromagnetic radiation have

been arranged in a spectrum called the Electromagnetic Spectrum

Recap of the theory of lightOnly a small part of the EM spectrum is visible

IR R O Y G B I V UV X-rays Gamma Rays

λred = 670 nanometres ( 1 nm = 1 x 10-9 m)

λviolet = 400 nanometres

Using c = fλ, find the frequency for red and violet light.

Blackbody RadiationAt the end of the 19th century, the spectrum of light emitted

by hot objects remained unexplained.All objects emit radiation and the total intensity α T4 where

T is in Kelvins. At lower temperatures we are unaware of this radiation as

its intensity is so low, however, at higher temperatures, we can first feel the heat (infrared radiation) if we are close enough. As the temperature continues to rise e.g. 1000K, objects glow like a stove or electric toaster element. At temperatures above 2000 K the glow is yellow or white such as a light bulb filament. This behaviour is similar for all incandescent solids.

The relative brightness of the glow given off i.e. the EM radiation emitted ,depends primarily on the temperature. The spectrum of emitted EM radiation shifts to higher frequencies

Heated objects give off light

www.freefoto.comfeps.as.arizona.edu/outreach/bbwein.html

Blackbody RadiationFrom Huygens in the late 1600’s to Maxwell in

the late 1800’s physicists had been studying light and EM radiation.

Maxwell’s Equations summarized the knowledge on electromagnetism and EM radiation

http://en.wikipedia.org/wiki/Maxwell's_equationsThey represented the equivalent of Newton’s

laws for EM radiationThe problem of blackbody radiation would upset

the established order in physics.

Blackbody RadiationWhile studying emission and absorption spectra of

gases, Gustav Kirchhoff and Robert Bunsen observed that when gases were heated to a high enough temperature, light of different frequencies was given off.

When white light was shone through the gases, they absorbed the same frequencies they emitted, so Kirchhoff reasoned that all objects absorb the same frequencies of radiation they emitted and further that since black objects absorb all frequencies of light, they should emit all frequencies when heated sufficiently

Blackbody RadiationSo a “blackbody” is a perfect radiator as it

emits the full spectrum of EM radiation .Blackbodies can be easily simulated in the

lab The Physics Hypertextbook™© 1998-2008 by Glenn Elert -- A Work in Progress feps.as.arizona.edu/outreach/bbwein.html

Blackbody RadiationThe graphs showed that as the temperature

of an incandescent body increased, the frequency of light emitted with he highest intensity becomes higher

Kirchhoff couldn’t explain the relationshipJosef Stefan showed that the power emitted

by a blackbody radiatorPα Temp4

This did not fit the experimental data completely.

Ultraviolet catastropheClassical physics was able to explain the

observed behaviour at low frequencies, but fell apart at higher frequencies, in particular in the UV (ultraviolet) part of the spectrum.

http://www.vectorsite.net/tpqm_01_01.png

Enter Quantum TheoryMax Planck, a student of Kirchhoff, was able to explain

the graph of frequencies of a blackbody radiator.He assumed that the energies of the oscillators in the

walls of the radiator were, in fact, discrete and that the energy levels were “quantized”

E = hf where h is a constant and f is the frequency of the radiation.

An oscillator could only have an energy level which was an integral multiple of hf

When the blackbody emitted radiation, it had to drop one or more levels and emit a unit or quantum of energy equal to the difference between allowed levels.

Quantum TheoryDespite the agreement of the data with

Planck’s theory, many physicists including Planck himself remained sceptical feeling that more evidence was required before accepting energy quantization.

The Photoelectric EffectDiscovered by accident when Hertz was investigating EM

(1887)Hertz apparatusSparks set up in transmitter circuit generated EM

radiation i.e. energy in receiver circuitWhen UV light was shone on metal electrodes, sparks

were enhanced- he didn’t know whyIn 1897, JJ Thomson discovered the electron and

physicists then suggested that UV light caused electrons to be elected from electrodes creating the conducting path.

Ejection of electrons by UV light became known as the photoelectric effect

Early Photoelectric Effect ExperimentsLenard (1902) set up apparatus as shown in your text

p. 845 and experimented with different frequencies of light and varying the polarity of the power supply.

He discovered the stopping potential i.e. the voltage which would oppose the flow of the photoelectrons.

He concluded that when the intensity of the light striking the emitted increases, the number of ejected electrons increases and that the max KE of the ejected electrons is determined only by the frequency of the light not the intensity.

The latter conclusion could not be explained by classical wave theory.

Einstein and the Photoelectric EffectLenard’s work raised even more questions from an already

sceptical physics communityEinstein (1905) proposed that light must be both absorbed and

emitted as packets (bundles) of energy called quanta or photons.

He said that E =hf is the energy of a photon and when a photon hits a metal surface, all its energy is absorbed by one electron. This meant that higher frequency light (photons) would be able to give more KE to the photoelectrons. Furthermore, increasing the intensity of the light would only change the number of photons not the energy of each photon.

Einstein further indicated that some of the photon’s energy must go into freeing the electron from the surface. The more tightly bound the electron, the more energy is required to liberate it from the surface. This is the work function of the metal.

Einstein and the Photoelectric EffectE = W + KE (max)hf = W + KE (max)KE (max) = hf – W this looks like y = mx + b with

a negative interceptRobert Millikan (1916) set out to prove Einstein

wrong, but his data confirmed Einstein’s proposalsThe x-intercepts on the graphs of Kinetic energy

vs frequency for different metals showed the threshold frequencies (minimum) for the different metals to reach the surface but not to exit the surface since they have no KE; they are drawn back into the metal.

The Electron VoltBecause the energies of photoelectrons are

fractions of a Joule (a large unit for the sub-atomic world), we use another unit called the electron volt (or eV)

Since E = qV, 1eV = (1e)(1V) = (1.602 x 10-

19 C)(1V)1eV = 1.602 x 10-19 JThe photoelectric effect was used in light

meters to measure the intensity of light.