PAPER No. : 8 AND PHYSICAL SPECTROSCOPY MODULE No. : 3 AND NATURE OF ELECTROMAGNETIC RADIATION- PARTICLE CHARACTER

Size: px

Start display at page:

Download "PAPER No. : 8 AND PHYSICAL SPECTROSCOPY MODULE No. : 3 AND NATURE OF ELECTROMAGNETIC RADIATION- PARTICLE CHARACTER"

Rhoda Miller
5 years ago
Views:

1 Subject Chemistry Paper No and Title Module No and Title Module Tag 8 and Physical Spectroscopy 3 and Nature of Electromagnetic Radiation- Particle Character CHE_P8_M3

2 TABLE OF CONTENTS 1. Learning Outcomes 2. Introduction 3. Nature of Electromagnetic Radiation- Particle Character 3.1 The Photoelectric Effect 3.2 Einstein s Explanation of the Photoelectric Effect 3.3 Einstein s Photoelectric Equation 3.4 Technology 4. Is Light a Wave or a Particle? 4.1 Photons 4.2 Matter Waves 5. Summary

1. Learning Outcomes In this module, we review the photoelectric effect, an important experiment that could not be explained on the basis of the wave aspect of radiation, a situation that led

3 1. Learning Outcomes In this module, we review the photoelectric effect, an important experiment that could not be explained on the basis of the wave aspect of radiation, a situation that led Einstein to postulate the existence of photons. We also discuss how this could explain observed phenomena related to the photoelectric effect. In addition, the idea of matter waves put forth by Louis de Broglie is also discussed. 2. Introduction Max Planck proposed the quantum nature of light in 1901 to explain the blackbody spectrum emitted by an object at a given temperature. It was as a matter of mathematical necessity not any actual belief that light consisted of discrete quanta. Einstein, on the other hand, took this mathematical trick, and interpreted it literally: if light could only possess energies which were integer multiples of the Planck discrete energy, E = hν, perhaps light was actually composed of discrete packets (photons), each possessing an energy hν. We begin by giving the introductory paragraphs from Albert Einstein s landmark paper "Übereinen die Erzeugung und Verwandlung des LichtesbetreffendenheuristischenGesichtspunkt." Annalen der Physik. Leipzig 17 (1905) 132; "On a Heuristic Viewpoint Concerning the Production and Transformation of Light."

4 It seems to me that the observation associated with black body radiation, fluorescence, the photoelectric effect, and other related phenomena associated with the emission or transformation of light are more readily understood if one assumes that the energy of light is discontinuously distributed in space. In accordance with the assumption to be considered here, the energy of a light ray spreading out from a point is not continuously distributed over an increasing space, but consists of a finite number of energy quanta which are localized at points in space, which move without dividing, and which can only be produced and absorbed as complete units. In the following I wish to present the line of thought and the facts which have led me to this point of view, hoping that this approach may be useful to some investigators in their research. Let us first look at the photoelectric experiment and its results and understand what led Einstein to make his landmark revelation. 3. Nature of Electromagnetic Radiation- Particle Character 3.1 The Photoelectric Effect In 1886 and 1887 Heinrich Hertz observed that ultraviolet (UV) light caused electrons to be emitted from the surface of a metal. Remember that Hertz was the one who discovered radiowaves. For his experiments to test Maxwell s electromagnetic theory, he required electromagnetic radiation having wavelengths of a few metres which could be measured in his laboratory. It was not possible to generate an alternating current of 100 MHz or so required for this purpose by mechanical generators, so he produced this high frequency AC by abruptly discharging a condenser (now known as capacitor) in the form of an electric spark. Using his spark-gap generator (Figure 1), he invented the earliest form of radio receiver, which works on a spark induced between two small spheres (he used polished brass knobs) in the receiver by a spark generated on another two spheres in the transmitter.

Figure 1: Hertz's radio wave generator (transmitter). The free standing structure on the right was a twometre high reflector with a spark gap and short dipole antenna at its focal point.

net/nfld1901/marconi-nfld.html His interesting observation was that the sensitivity of his spark-gap device could be increased by illuminating it with visible or ultraviolet light.

5 Figure 1: Hertz's radio wave generator (transmitter). The free standing structure on the right was a twometre high reflector with a spark gap and short dipole antenna at its focal point. The apparatus on the table was an induction coil to generate a high voltage spark at the gap. Adapted from "Electric Waves", by Heinrich Hertz, MacMillan & Co. (1900). His interesting observation was that the sensitivity of his spark-gap device could be increased by illuminating it with visible or ultraviolet light. Later, the discovery of the electron by J.J. Thomson ( ) in 1897 confirmed that this increased sensitivity was the result of light pushing out electrons from the metal. While this was interesting, it was hardly surprising! Electromagnetic radiation carries energy and this could be used to push out the tiny particles of negative charge from the surface of the metal ion to which they were loosely bound anyway. However, subsequent experiments on the photoelectric effect produced amazing results that did not fit into the classical theories and turned physics upside down. In 1902, Philipp von Lenard (Hertz s assistant) noticed that the kinetic energy of the emitted electrons was independent of the intensity of the light. This did not make sense. In classical wave theories of light, more intense sources contained more energy that would be transferred to the outgoing electrons. Using classical theory, as the intensity of the light increases, the electrons on the surface of the metal should oscillate more vigorously. At some point, the electrons will have sufficient energy to escape the metal.

6 He found that the intensity of the incident light had no effect on the maximum kinetic energy of the photoelectrons. Those ejected from exposure to a very bright light had the same energy as those ejected from exposure to a very dim light of the same frequency. In keeping with the law of conservation of energy, however, more electrons were ejected by a bright source than a dim source- the current was proportional to the intensity. Later experiments, e.g. those by Robert Millikan ( ), revealed another puzzling aspect light with frequencies below a certain cut-off value, called the threshold frequency, failed to eject photoelectrons from the metal, no matter how high the intensity of the source. It was observed that red light, whatever its intensity, did not produce a current, while blue light (higher frequency than red) of even small intensity did the job, i.e. it did not matter whether the light was bright or dim, what mattered was its frequency.

7 The observations can be summed up as follows: Only light with a frequency greater than a certain threshold produces a current Current begins almost instantaneously, even for light of very low intensity Current is proportional to the intensity of the incident light A typical photoelectric experiment could produce the following results: red light would not produce photoelectrons, even if it were bright, green light (intermediate frequency) would produce photoelectrons (even if it was very dim), blue light would produce photoelectrons with greater kinetic energies than those ejected by green light. Note that all metals do not eject photoelectrons with visible light- most require UV radiation and semiconductors can even produce photoelectrons using near-ir radiation. Now, where did the existing theories fail to explain these observations? Let us revisit the classical picture of electromagnetic radiation. Scientists of the nineteenth century were in no doubt that all electromagnetic radiation is a transverse, electromagnetic wave. Numerous optical phenomena, such as diffraction, interference, polarization, reflection and refraction were evidence for this. A wave is an oscillation in space and time that transfers energy without transferring matter. In other words, the wave is undergoing simple harmonic motion (SHM), for which the energy is proportional to the square of the amplitude. In the case of our electromagnetic wave, the intensity of the radiation is proportional to the square of the amplitude of its electric field, i.e.:! I E 2 This means that the energy of the wave is proportional to its intensity- brighter the light, more is its energy. Classical thinking would imagine metals as having a sea of electrons on the surface. A large wave (bright light) could push an electron from the surface, while a weak wave (dim light) could not. This wave analogy has no place for frequency. The photoelectric experiments

8 suggested that tiny ripples could push a boat across the Indian Ocean, provided they had the correct frequency, while tornadoes would do no harm. The second observation, that current begins almost instantaneously, also had no explanation. Classical thinking would suggest that an electron absorbing low intensity light would start oscillating more rapidly as it absorbed more energy from light. It would continue absorbing light until it had enough energy to escape from the surface- but this does not happen. As soon as light of high frequency falls on the surface, an electron is ejected in almost no time (~ 1 ns). It was as if in a sea full of boats, all the energy of a wave is expended on a single boat, which kicks off, instead of being distributed on all the boats. 3.2 Einstein s Explanation of the Photoelectric Effect Enter Einstein (1905) and his conjecture that light is composed of discrete packets (photons), each possessing an energy hν. If this conjecture were true, it would have the following consequences in the photoelectric effect: 1) When a single photon interacts with a single electron, it can only transfer an energy hν to that electron. Therefore, if the light intensity is increased, the number of electrons emitted should increase, but the kinetic energy of an individual electron will be unchanged. 2) If the energy of an incident photon is less than the binding energy holding an electron in the surface of the metal, no electrons can be emitted, even if the intensity (number) of the incident photons is increased. In practice, we call this binding energy in a metal surface the work function (often denoted as φ). Different metals have different work functions akin to the ionization energy. 3) If a photon has an energy greater that the metal s work function, an electron may be emitted, but the maximum kinetic energy the electron can possess after escaping the surface of the metal is equal to the photon energy, hν, minus the metal work function. These predictions were in complete agreement with experiment, and Einstein s interpretation of the photoelectric effect paved the way for modern quantum mechanics. us now elaborate the new ideas: Two factors affect the maximum kinetic energy of photoelectrons the frequency of the incident radiation and the material of the surface. As can be seen from the figure below, the three metals potassium, beryllium and titanium have different threshold frequencies, only potassium dipping into the visible. This shows that the threshold frequency is a function of the material. Above the threshold, the electron energy is a linear function of the frequency, but the slope of all three lines is the same, equal to Planck s constant, which shows that the energy-frequency relationship is the same for all materials.

The explanation of the photoelectric effect earned Albert Einstein (1879-1955) (Germany- Switzerland) the Nobel Prize in 1921 "for services to Theoretical Physics, and especially of the law of the

9 The explanation of the photoelectric effect earned Albert Einstein ( ) (Germany- Switzerland) the Nobel Prize in 1921 "for services to Theoretical Physics, and especially of the law of the photoelectric effect''. 3.3 Einstein s Photoelectric Equation Einstein's formula relates the maximum kinetic energy (E k ) of the photoelectrons to the frequency of the absorbed photons (ν) and the threshold frequency (ν 0 ) of the photoemissive surface. (This formula is only approximate, however, and a minor correction is needed for the Compton Effect.) E k = h(ν ν 0 ) or if you prefer, to the energy of the absorbed photons (E) and the work function (φ) of the surface E k = E φ where the first term is the energy of the absorbed photons (E) with frequency (ν) or wavelength (λ) hc E = hν = λ and the second term is the work function (φ) of the surface with threshold frequency (ν 0 ) or threshold wavelength (λ 0 )

10 hc φ = h ν 0 = λ 0 where φ is the energy needed to escape the metal. If one actually performs the experiment the result is: The maximum kinetic energy (E k ) of the photoelectrons (with charge e) can be determined from the stopping potential (V). Since V joule. W Ek = =, E k = ev. If the electron charge is expressed in coulomb, the energy is in q e

11 1 = mv = hν φ 2 E k 2 and hν 0 = φ The rate (n/t) at which photoelectrons (with charge e) are emitted from a photoemissive surface can be determined from the photoelectric current (I). q ne n I = = = t t t I e Figure 2. Diagram of the maximum kinetic energy as a function of the frequency of light on zinc The photoelectric effect is widely used as an experimental tool today. There is an entire field of study, known as photoelectron spectroscopy, where monochromatic light sources, ranging from the visible to X-rays, are used to photo-excite e - from a given sample (metal, semiconductor or insulator). The energy distribution of the emitted electrons is measured. Because of Einstein s explanation of the photoelectric effect, the researcher can then work backwards, since the photon energy is known, and determine the binding energy that a detected electron originated from within the sample. This skill has been used to study the conduction electrons of high temperature superconductors, to understand the interactions at interfaces between metals and semiconductors used in electronic devices, and to investigate chemical reactions that take place on the surfaces of metals (of great interest in the field of catalysis) 3.4 Technology The photoelectric effect has been translated to technology, as in "electric eye", light metre, movie film audio track photoconductivity: an increase in the electrical conductivity of a nonmetallic solid when exposed to electromagnetic radiation. The increase in conductivity is due to the addition of free electrons liberated by collision with photons. The rate at which free electrons are

12 generated and the time over which they remain free determines the amount of the increase. photovoltaics: the ejected electron travels through the emitting material to enter a solid electrode in contact with the photoemitter (instead of travelling through a vacuum to an anode) leading to the direct conversion of radiant energy to electrical energy photostatic copying Now we ask a key question. 4. Is Light a Wave or Particle? 4.1 Photons The answer is both, depending on what question you ask: it has a wave' aspect and a particle aspect. Light may show properties of a wave or of a particle, called a photon. The term "photon" was proposed by G. N, Lewis in Light as a wave: Light as a particle: νλ = c E = hν Photon Let us examine the evidences for both: Newton (1680) explained light as a particle of energy. In reflection and refraction, light behaved as a particle. Young (~ 1800) showed that light interfered with itself. Therefore, it must be a wave. Reflection and refraction could be explained by light being a wave. Maxwell (1850) showed that light is a form of high frequency electromagnetic wave. Einstein (1905) showed that in the photoelectric effect (light causing electrons to be emitted from a metal surface) light must act as a particle. Planck (1900) developed a model that explained light as a quantization of energy. Energy of a light wave is present in bundles of energy called photons; the energy is said to be quantized into the photons. Photons move with the speed of light have no mass are electrically neutral they carry momentum p = hν / c energy of a photon or electromagnetic wave: E = hν = hc / λ This equation relates the energy of each photon of the radiation to the electromagnetic wave characteristics (ν and λ).

13 Therefore, light must be regarded as having a dual nature; in some cases light acts as a wave; in others it acts like a particle. NOTE: The quantized nature of light is most important when considering absorption and emission of electromagnetic radiation. On macroscopic scales, we can treat a large number of photons as a wave. When dealing with subatomic phenomenon, we are often dealing with a single photon, or a few. In this case, you cannot use the wave description of light. It doesn t work! Problem 1: A light bulb of 100 W emits at 0.5 µm. How many photons are emitted per second? Solution: The energy of one photon is ε photon = hc 0 /λ; thus, using that 100 W = 100 J/s, the number of photons per second, N, is (Js ) (m) ( ) = λ N s = = h(js) c (ms ) NOTE: Large number of photons is required because Plank s constant h is very small!!! 4.2 Matter Waves Louis de Broglie (1924) extended the concept and proposed that if light can act as both wave and particle, why cannot matter also act as waves? He gave the idea of matter waves, and

hypothesized that the wavelength associated with a particle of mass m moving with a speed v is given by λ = h / mv = h / p, where p is the momentum of the particle.

$diffraction! He was promptly proved right by Davisson and Germer, who accelerated electrons onto a crystal and observed wave diffraction, as would be seen with X-rays.$

14 hypothesized that the wavelength associated with a particle of mass m moving with a speed v is given by λ = h / mv = h / p, where p is the momentum of the particle. When asked in his PhD viva voce examination how his idea of matter waves could be verified, he replied that the wavelengths of electrons would be comparable to the crystal spacings and could cause diffraction! He was promptly proved right by Davisson and Germer, who accelerated electrons onto a crystal and observed wave diffraction, as would be seen with X-rays. For this hypothesis, de Broglie was awarded the Nobel Prize in Problem 2: Calculate the de Broglie wavelength for an electron in an electron microscope accelerated with a potential of 100 V. Solution: A charge q accelerated through a potential V acquires a kinetic energy E k = qv. Therefore, E k = C 100 V = J. The kinetic energy can be related to the linear momentum because E k = ½mv 2 and p = mv. Therefore, 31 p 2m e E = 2( kg)( J) = kg m s -1. = k Hence, according to the de Broglie s relation, λ = h / p = ( J s) /( kg m s 1 ) = m. This is similar to the spacing in crystals. So, we have wave-particle duality X-rays and electrons show similar behaviour!

15 The electron wave or particle was the Dr. Jekyll and Mr. Hyde of physics So electrons can be manipulated by light. Electrons wiggle up and down as light passes by. It is a transverse wave. In essence, all matter gets where its wave can go but appears as a particle when it gets there. Until it gets there, it is wherever its (diffuse) matter wave is. Worse still, it makes its own matter wave, like God surfing. Nothing in our everyday life behaves this way, but this is true for atom sized particles. Fortunately, it does not apply to larger sized particles because their momenta are so large that the wavelength is extremely small, too small to diffract anything so you do not see people spontaneously breaking into a rainbow! Nobel Laureate Richard Feynman said it best when he suggested "Do not keep saying to yourself, if you can possibly avoid it, 'but how can it be like that?' because you will get 'down the drain' into a blind alley from which nobody has escaped. Nobody knows how it can be like that." Imagine the confusion in the minds of the scientists of the time! They could but make the most of it, and went around with woebegone faces sadly complaining that on Mondays, Wednesdays and Fridays they must look on light as a wave; on Tuesdays, Thursdays and Saturdays as a particle. On Sundays they simply prayed. -Banesh Hoffmann (1947), The Strange Story of the Quantum, Summary The photoelectric experiments produced amazing results that did not fit into the classical theories and turned physics upside down. The kinetic energy of the emitted electrons was found to be independent of the intensity of the light.

16 The light with frequencies below a certain cut-off value, called the threshold frequency, failed to eject photoelectrons from the metal, no matter how high the intensity of the source. Two factors that affect the maximum kinetic energy of photoelectrons are the frequency of the incident radiation and the material of the surface. Light may show properties of a wave or of a particle, called a photon. Louis de Broglie gave the idea of matter waves, and hypothesized that the wavelength associated with a particle of mass m moving with a speed v is given by λ = h / mv = h / p, where p is the momentum of the particle.

Heinrich Hertz, a German physicist, achieved the first experimental demonstration of EM waves in 1887.

Heinrich Hertz, a German physicist, achieved the first experimental demonstration of EM waves in 1887. 9.4.2-1(i) Hertz s first radio wave transmission demonstration Maxwell In 1865 James Clerk Maxwell predicted the existence of electromagnetic waves. He said that an accelerating charge would produce a