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3.33.3Origins of Quantum TheoryMax Planck (1858–1947) is credited with starting the quantum revolution with a sur-prising interpretation of the experimental results obtained from the study of the lightemitted by hot objects, started by his university teacher, Gustav Kirchhoff (Figure 1).Kirchhoff was interested in the light emitted by blackbodies. The term “blackbody” is usedto describe an ideal, perfectly black object that does not reflect any light, and emits var-ious forms of light (electromagnetic radiation) as a result of its temperature.

Planck’s Quantum HypothesisAs a solid is heated to higher and higher temperatures, it begins to glow. Initially, itappears red and then becomes white when the temperature increases. Recall that whitelight is a combination of all colours, so the light emitted by the hotter object must nowbe accompanied by, for example, blue light. The changes in the colours and the corre-sponding spectra do not depend on the composition of the solid.

If electronic instruments are used to measure the intensity (brightness) of the differentcolours observed in the spectrum of the emitted light, a typical bell-shaped curve is obtained.

For many years, scientists struggled to explain the curves shown in Figure 2. Somewere able to create an equation to explain the intensity curve at one end or the other, butnot to explain the overall curve obtained from experiments. In 1900 Planck developed amathematical equation to explain the whole curve, by using a radical hypothesis. Plancksaw that he could obtain agreement between theory and experiment by hypothesizingthat the energies of the oscillating atoms in the heated solid were multiples of a smallquantity of energy; in other words, energy is not continuous. Planck was reluctant topursue this line of reasoning, and so it was Albert Einstein who later pointed out thatthe inevitable conclusion of Planck’s hypothesis is that the light emitted by a hot solid isalso quantized — it comes in “bursts,” not a continuous stream of energy (Figure 3).One little burst or packet of energy is known as a quantum of energy.

This is like dealing with money — the smallest quantity of money is the penny and anyquantity of money can be expressed in terms of pennies; e.g., $1.00 is 100 pennies. Ofcourse, there are other coins. The $1.00 can be made up of two quarters, three dimes, threenickels, and five pennies.We can apply this thought to light.You could think of the coins rep-resenting the energy of the light quanta — the penny is infrared, the nickel is red, the dimeis blue, and the quarter is ultraviolet radiation. Heat (without colour) would then be emitted

Figure 1Kirchhoff and other experimentersstudied the light given off by heatedobjects, such as this red-hot furnace.

Hot Solids (p. 210)What kind of light is given off whena solid is heated so that it becomes“white hot”?

ACTIVITY 3.3.1

quantum a small discrete, indivisiblequantity (plural, quanta); a quantumof light energy is called a photon

visible

Inte

nsit

y

UV IR

(spectrum)

white hot

classical theory

red hot

V R

Figure 2The solid lines show the intensity of the colours of light emittedby a red-hot wire and a white-hot wire. Notice how the curvebecomes higher and shifts toward the higher-energy UV as thetemperature increases. The dotted line represents the pre-dicted curve for a white-hot object, according to the existingclassical theory before Planck.

Figure 3Scientists used to think that as theintensity or brightness of lightchanges, the total energy increasescontinuously, like going up the slopeof a smooth hill. As a consequenceof Planck’s work, Einstein suggestedthat the slope is actually a staircasewith tiny steps, where each step is aquantum of energy.

Intensity

Ener

gy

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as pennies only, red-hot radiation would include nickels, white-hot radiation would adddimes, and blue-hot would likely include many more dimes and some quarters. An inter-pretation of the evidence from heating a solid is that a sequence of quanta emissions fromIR to red to blue to UV occurs — pennies, to nickels, to dimes, to quarters, by analogy.

A logical interpretation is that as the temperature is increased, the proportion of eachlarger quantum becomes greater. The colour of a heated object is due to a complex com-bination of the number and kind of quanta.

Although Planck (Figure 4) was not happy with his own hypothesis, he did what hehad to do in order to get agreement with the ultimate authority in science — the evidencegathered in the laboratory. Planck thus started a trend that helped to explain other exper-imental results (for example, the photoelectric effect) that previously could not beexplained by classical theory.

The Photoelectric EffectThe nature of light has been the subject of considerable debate for centuries. Greek philoso-phers around 300 B.C. believed light was a stream of particles. In the late 17th century, exper-iments led the Dutch scientist Christiaan Huygens to propose that light can best be explainedas a wave. Not everyone agreed. The famous English scientist, Isaac Newton, bitterly opposedthis view and continued to try to explain the properties of light in terms of minute particlesor “corpuscles.”However, mounting evidence from experiments with, for example, reflection,refraction, and diffraction clearly favoured the wave hypothesis over the particle view.

In the mid-19th century, James Maxwell produced a brilliant theory explaining the knownproperties of light, electricity, and magnetism. He proposed that light is an electromagneticwave composed of electric and magnetic fields that can exert forces on charged particles. Thiselectromagnetic-wave theory, known as the classical theory of light, eventually becamewidely accepted when new experiments supported this view. Most scientists thought this wasthe end of the debate about the nature of light — light is (definitely) an electromagnetic waveconsisting of a continuous series of wavelengths (Figure 5).

102104

104 106 108 1010 1012 1014 1016 1018 1020 1022 1024

microwaves

radiowaves X raysinfrared gamma rays

UV cosmic rays

frequency, f (Hz) visible light

Electromagnetic Spectrum

wavelength, λ (m)10–2 10–41 10–6 10–8 10–10 10–12 10–14 10–16

PracticeUnderstanding Concepts

1. The recommended procedure for lighting a laboratory burner is to close the air inlet,light the burner, and then gradually open the air inlet. What is the initial colour of theflame with the air inlet closed? What is the final colour with sufficient air? Which isthe hotter flame?

2. How would observations of a star allow astronomers to obtain the temperature of the star?

3. Draw staircase diagrams (like Figure 3) to show the difference between low-energyred light quanta versus higher-energy violet light quanta.

4. Liquids and solids, when heated, produce continuous spectra. What kind of spectrumis produced by a heated gas?

Figure 5The electromagnetic spectrum, originally predicted by Maxwell,includes all forms of electromag-netic radiation from very shortwavelength gamma (�) rays to ordinary visible light to very longwavelength radio waves.

Figure 4Max Planck was himself puzzled bythe "lumps" of light energy. He pre-ferred to think that the energy wasquantized for delivery only, just likebutter, which is delivered to storesonly in specific sizes, even though itcould exist in blocks of any size.

Photon EnergyThe energy, E, of a photon of light isthe product of Planck’s constant, h,and the frequency, f, of the light. If youare a StarTrek fan, you will recognizethat the creators of this popular seriesborrowed the photon term to invent a“photon torpedo” that fires bursts orquanta of light energy at enemy ships.An interesting idea, but not practical.

DID YOU KNOW ??

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The photoelectric effect is one of the key experiments and stories leading to quantumtheory. Heinrich Hertz discovered the photoelectric effect by accident in 1887. It involvesthe effect of electromagnetic radiation or light on substances, particularly certain metals.Hertz studied this effect qualitatively but had no explanation for it.

Although Heinrich Hertz described his discovery of the photoelectric effect (Figure 6)as minor, it was to have a major contribution in changing the accepted, classical theory oflight. According to the classical theory, the brightness (intensity) of the light shone on themetal would determine the kinetic energy of the liberated electrons; the brighter the light,the greater the energy of the electrons ejected. This prediction was shown to be false. Furtherexperimental work showed that the frequency (colour/energy) of the light was the mostimportant characteristic of the light in producing the effect. Classical theory was thereforeunacceptable for explaining the photoelectric effect.

Albert Einstein was awarded the Nobel Prize in 1905 for using Planck’s idea of aquantum of energy to explain the photoelectric effect. He reasoned that light consistedof a stream of energy packets or quanta—later called photons. A photon of red lightcontains less energy than a photon of UV light (Figure 7). Einstein suggested that the ejec-tion of an electron from the metal surface could be explained in terms of a photon–electron collision. The energy of the photon is transferred to the electron. Some of thisenergy is used by the electron to break free from the atom and the rest is left over askinetic energy of the ejected electron. The electron cannot break free from the atomunless a certain minimum quantity of energy is absorbed from a single photon.

An electron held in an atom by electrostatic forces is like a marble trapped staticallyin a bowl. If you bang the bowl (with incrementally larger bumps), the marble can movehigher from rest in the bowl, but may still be trapped. A certain, minimum quantity ofpotential energy is required by the marble to escape from the bowl (Figure 8).This explains why the energy of the electrons produced by the photoelectric effect isindependent of light intensity. If one electron absorbs one photon, then the photonenergy (related only to the type of light) needs to be great enough for the electron to beable to escape. No electrons are detected at low photon energies because the energy ofthe single photon captured was insufficient for the electron to escape the metal. Thisquantum explanation worked, where no classical explanation could. Quantum theory

Section 3.3

Figure 6In the photoelectric effect, lightshining on a metal liberates elec-trons from the metal surface. Theammeter (A) records the electriccurrent (the number of electrons persecond) in the circuit.

The Photoelectric Effect (p. 209)The photoelectric effect has hadimportant modern applications suchas solar cells and X-ray imaging. Youcan investigate it using an electro-scope.

INVESTIGATION 3.3.1

photoelectric effect the release ofelectrons from a substance due tolight striking the surface of a metal

photon a quantum of light energy

Aphotocurrent

radiant energy

collectorliberated electronsmetal plate

Figure 7Each photon of light has a differentenergy, represented by the relativesizes of the circles.

Ener

gy

red

yellow

blue

UVUVUV

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K

red photon

UV photon

Na Li

electron gains energybut is still trapped

electron escapesfrom atom

e� e� e�

e�

e�

e�

e�

(a)

E

(b)

(c)

Figure 8(a) Using a bowl analogy, different

atoms would be representedwith bowls of different depths.

(b) For most atoms, the energy of ared photon is not great enoughto boost the electron (marble)out of the atom (bowl). Theelectron can absorb the energybut is still stuck in the atom.This process simply results inthe heating of the sample.

(c) A higher-energy photon, suchas a UV photon, has more thanenough energy to boost theelectron out of many atoms.

received a huge boost in popularity for explaining this and other laboratory effects at theatomic and subatomic levels.

Quantum theory is heralded as one of the major scientific achievements of the 20thcentury. There were results from many scientific experiments that could not be explainedby classical chemistry and physics, but these experimental results could be explained byquantum theory.

Two of the experiments leading to quantum theory are summarized below, but therewere many more that could only be explained using quantum theory.

Creating Quantum TheorySUMMARY

Table 1

Key experimental work Theoretical explanation Quantum theory

Kirchhoff (1859): Planck (1900): The energy Electromagnetic energy blackbody radiation from a blackbody is is not infinitely subdivisible;

quantized; i.e., restricted to energy exists as packets orwhole number multiples of quanta, called photons. certain energy A photon is a small packet

Hertz (1887): the photo- Einstein (1905): The size of of energy corresponding to

electric effect a quantum of a specific frequency of

electromagnetic energy light (E = hf).

depends directly on its frequency; one photon ofenergy ejects one electron

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Section 3.3

Section 3.3 QuestionsUnderstanding Concepts

1. State the two important experimental observations thatestablished the quantum theory of light.

2. Although Einstein received the Nobel Prize for his explana-tion of the photoelectric effect, should Max Planck be con-sidered the father of quantum theory?

3. Write a brief description of the photoelectric effect experi-ment.

4. Distinguish between the terms “quantum” and “photon.”

Applying Inquiry Skills

5. What effect does the type or colour of light have on therelease of electrons from a sodium metal surface?(a) Write a brief experimental design to answer this ques-

tion, based on Figure 6. Be sure to identify all variables.(b) Would you expect all colours of light to release elec-

trons from the sodium metal? Justify your answer, ingeneral terms, using the idea of photons.

Extension

6. Einstein won the Nobel Prize in 1921 for explaining the photoelectric effect in 1905. Einstein calculated the energyof an incoming photon from the Planck equation

E � hf

where E is energy in joules (J), h is Planck’s constant (6.6 x 10–34 J/Hz), and f is the frequency in hertz (Hz) oflight shining on the metal.(a) If the minimum frequency of light required to have an

electron escape from sodium is 5.5 � 1014 Hz, calcu-late the energy of photons of this frequency.

(b) What is the minimum energy of the quantum leap thatan electron makes to escape the sodium atom as aphotoelectron?

7. Ultraviolet (UV) light that causes tanning and burning ofthe skin has a higher energy per photon than infrared (IR)light from a heat lamp.(a) Use the Planck equation from the previous question to

calculate the energy of a 1.5 � 1015 Hz UV photon anda 3.3 � 1014 Hz IR photon.

(b) Compare the energy of the UV and IR photons, as aratio.

(c) From your knowledge of the electromagnetic spectrum,how does the energy of visible-light photons and X-rayphotons compare with the energy of UV and IR photons?