Origins of Quantum Theory

Transcription

1 Origins of Quantum Theory 3.3 Max Planck ( ) is credited with starting the quantum revolution with a surprising interpretation of the experimental results obtained from the study of the light emitted 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 used to describe an ideal, perfectly black object that does not reflect any light, and emits various forms of light (electromagnetic radiation) as a result of its temperature. Planck s Quantum Hypothesis As a solid is heated to higher and higher temperatures, it begins to glow. Initially, it appears red and then becomes white when the temperature increases. Recall that white light is a combination of all colours, so the light emitted by the hotter object must now be accompanied by, for example, blue light. The changes in the colours and the corresponding spectra do not depend on the composition of the solid. If electronic instruments are used to measure the intensity (brightness) of the different colours 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. Some were able to create an equation to explain the intensity curve at one end or the other, but not to explain the overall curve obtained from experiments. In 1900 Planck developed a mathematical equation to explain the whole curve, by using a radical hypothesis. Planck saw that he could obtain agreement between theory and experiment by hypothesizing that the energies of the oscillating atoms in the heated solid were multiples of a small quantity of energy; in other words, energy is not continuous. Planck was reluctant to pursue this line of reasoning, and so it was Albert Einstein who later pointed out that the inevitable conclusion of Planck s hypothesis is that the light emitted by a hot solid is also 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 any quantity of money can be expressed in terms of pennies; e.g., $1.00 is 100 pennies. Of course, there are other coins. The $1.00 can be made up of two quarters, three dimes, three nickels, and five pennies. We can apply this thought to light.you could think of the coins representing the energy of the light quanta the penny is infrared, the nickel is red, the dime is blue, and the quarter is ultraviolet radiation. Heat (without colour) would then be emitted Figure 1 Kirchhoff and other experimenters studied the light given off by heated objects, such as this red-hot furnace. ACTIVITY Hot Solids (p. 210) What kind of light is given off when a solid is heated so that it becomes white hot? quantum a small discrete, indivisible quantity (plural, quanta); a quantum of light energy is called a photon Energy Intensity Intensity V (spectrum) white hot visible R classical theory red hot IR Figure 3 Scientists used to think that as the intensity or brightness of light changes, the total energy increases continuously, like going up the slope of a smooth hill. As a consequence of Planck s work, Einstein suggested that the slope is actually a staircase with tiny steps, where each step is a quantum of energy. Figure 2 The solid lines show the intensity of the colours of light emitted by a red-hot wire and a white-hot wire. Notice how the curve becomes higher and shifts toward the higher-energy as the temperature increases. The dotted line represents the predicted curve for a white-hot object, according to the existing classical theory before Planck. Atomic Theories 169

2 DID YOU KNOW? Photon Energy The energy, E, of a photon of light is the product of Planck s constant, h, and the frequency, f, of the light. If you are a StarTrek fan, you will recognize that the creators of this popular series borrowed the photon term to invent a photon torpedo that fires bursts or quanta of light energy at enemy ships. An interesting idea, but not practical. as pennies only, red-hot radiation would include nickels, white-hot radiation would add dimes, and blue-hot would likely include many more dimes and some quarters. An interpretation of the evidence from heating a solid is that a sequence of quanta emissions from IR to red to blue to occurs pennies, to nickels, to dimes, to quarters, by analogy. A logical interpretation is that as the temperature is increased, the proportion of each larger quantum becomes greater. The colour of a heated object is due to a complex combination of the number and kind of quanta. Although Planck (Figure 4) was not happy with his own hypothesis, he did what he had to do in order to get agreement with the ultimate authority in science the evidence gathered in the laboratory. Planck thus started a trend that helped to explain other experimental results (for example, the photoelectric effect) that previously could not be explained by classical theory. Practice Figure 4 Max Planck was himself puzzled by the "lumps" of light energy. He preferred to think that the energy was quantized for delivery only, just like butter, which is delivered to stores only in specific sizes, even though it could exist in blocks of any size. Figure 5 The electromagnetic spectrum, originally predicted by Maxwell, includes all forms of electromagnetic radiation from very short wavelength gamma ( ) rays to ordinary visible light to very long wavelength radio waves. Understanding 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 the flame with the air inlet closed? What is the final colour with sufficient air? Which is the 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-energy red light quanta versus higher-energy violet light quanta. 4. Liquids and solids, when heated, produce continuous spectra. What kind of spectrum is produced by a heated gas? The Photoelectric Effect The nature of light has been the subject of considerable debate for centuries. Greek philosophers around 300 B.C. believed light was a stream of particles. In the late 17th century, experiments led the Dutch scientist Christiaan Huygens to propose that light can best be explained as a wave. Not everyone agreed. The famous English scientist, Isaac Newton, bitterly opposed this view and continued to try to explain the properties of light in terms of minute particles or 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 known properties of light, electricity, and magnetism. He proposed that light is an electromagnetic wave composed of electric and magnetic fields that can exert forces on charged particles. This electromagnetic-wave theory, known as the classical theory of light, eventually became widely accepted when new experiments supported this view. Most scientists thought this was the end of the debate about the nature of light light is (definitely) an electromagnetic wave consisting of a continuous series of wavelengths (Figure 5). Electromagnetic Spectrum frequency, f (Hz) visible light microwaves cosmic rays radiowaves infrared X rays gamma rays 10 4 wavelength, λ (m) Chapter 3

3 Section 3.3 radiant energy INVESTIGATION The Photoelectric Effect (p. 209) The photoelectric effect has had important modern applications such as solar cells and X-ray imaging. You can investigate it using an electroscope. metal plate liberated electrons A photocurrent collector Figure 6 In the photoelectric effect, light shining on a metal liberates electrons from the metal surface. The ammeter (A) records the electric current (the number of electrons per second) in the circuit. The photoelectric effect is one of the key experiments and stories leading to quantum theory. Heinrich Hertz discovered the photoelectric effect by accident in It involves the 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 of light. According to the classical theory, the brightness (intensity) of the light shone on the metal 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. Further experimental work showed that the frequency (colour/energy) of the light was the most important characteristic of the light in producing the effect. Classical theory was therefore unacceptable for explaining the photoelectric effect. Albert Einstein was awarded the Nobel Prize in 1905 for using Planck s idea of a quantum of energy to explain the photoelectric effect. He reasoned that light consisted of a stream of energy packets or quanta later called photons. A photon of red light contains less energy than a photon of light (Figure 7). Einstein suggested that the ejection 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 this energy is used by the electron to break free from the atom and the rest is left over as kinetic energy of the ejected electron. The electron cannot break free from the atom unless 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 statically in a bowl. If you bang the bowl (with incrementally larger bumps), the marble can move higher from rest in the bowl, but may still be trapped. A certain, minimum quantity of potential 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 is independent of light intensity. If one electron absorbs one photon, then the photon energy (related only to the type of light) needs to be great enough for the electron to be able to escape. No electrons are detected at low photon energies because the energy of the single photon captured was insufficient for the electron to escape the metal. This quantum explanation worked, where no classical explanation could. Quantum theory photoelectric effect the release of electrons from a substance due to light striking the surface of a metal photon a quantum of light energy Energy blue yellow red Figure 7 Each photon of light has a different energy, represented by the relative sizes of the circles. Atomic Theories 171

4 Figure 8 (a) Using a bowl analogy, different atoms would be represented with bowls of different depths. (a) E K Na Li (b) For most atoms, the energy of a red photon is not great enough to boost the electron (marble) out of the atom (bowl). The electron can absorb the energy but is still stuck in the atom. This process simply results in the heating of the sample. (b) red photon electron gains energy but is still trapped (c) A higher-energy photon, such as a photon, has more than enough energy to boost the electron out of many atoms. (c) photon electron escapes from atom received a huge boost in popularity for explaining this and other laboratory effects at the atomic and subatomic levels. Quantum theory is heralded as one of the major scientific achievements of the 20th century. There were results from many scientific experiments that could not be explained by classical chemistry and physics, but these experimental results could be explained by quantum theory. Two of the experiments leading to quantum theory are summarized below, but there were many more that could only be explained using quantum theory. SUMMARY Creating Quantum Theory 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 or whole 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 of energy ejects one electron 172 Chapter 3

5 Section 3.3 Section 3.3 Questions Understanding Concepts 1. State the two important experimental observations that established the quantum theory of light. 2. Although Einstein received the Nobel Prize for his explanation of the photoelectric effect, should Max Planck be considered the father of quantum theory? 3. Write a brief description of the photoelectric effect experiment. 4. Distinguish between the terms quantum and photon. Applying Inquiry Skills 5. What effect does the type or colour of light have on the release of electrons from a sodium metal surface? (a) Write a brief experimental design to answer this question, based on Figure 6. Be sure to identify all variables. (b) Would you expect all colours of light to release electrons from the sodium metal? Justify your answer, in general terms, using the idea of photons. Extension 6. Einstein won the Nobel Prize in 1921 for explaining the photoelectric effect in Einstein calculated the energy of an incoming photon from the Planck equation where E is energy in joules (J), h is Planck s constant (6.6 x J/Hz), and f is the frequency in hertz (Hz) of light shining on the metal. (a) If the minimum frequency of light required to have an electron escape from sodium is Hz, calculate the energy of photons of this frequency. (b) What is the minimum energy of the quantum leap that an electron makes to escape the sodium atom as a photoelectron? 7. Ultraviolet () light that causes tanning and burning of the 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 Hz photon and a Hz IR photon. (b) Compare the energy of the and IR photons, as a ratio. (c) From your knowledge of the electromagnetic spectrum, how does the energy of visible-light photons and X-ray photons compare with the energy of and IR photons? E hf Atomic Theories 173