Chapter 2 early quantum theory
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This document provides an overview of key topics in early quantum theory that students should understand, including: - Electrons, J.J. Thompson's experiment determining the electron, and Millikan's experiment measuring the charge of an electron. - De Broglie's relation connecting the wavelength of a particle to its momentum. - Wave-particle duality and the principle of complementarity stating that particles can behave as both waves and particles. - Planck's quantum hypothesis that the energy of atomic oscillations is quantized in integer multiples of Planck's constant.
Chapter 2 early quantum theory
- 2. SCOPE OF STUDY 7 sub- topics students should learn and understand : Electrons J.J. Thompson’s experiment, Milikan experiment De Broglie Relation Wave-particle duality; the Principle of Complementarily Wave nature of matter Electron diffraction Planck’s quantum hypothesis
- 3. introduction Quantum Physics: developed early 20th century, in response to shortcomings of classical physics in describing certain phenomena (blackbody radiation, photoelectric effect, emission and absorption spectra…) describes “small” objects (e.g. atoms and their constituents) QP is “weird and counterintuitive” “Those who are not shocked when they first come across quantum theory cannot possibly have understood it” (Niels Bohr) “Nobody feels perfectly comfortable with it “ (Murray Gell-Mann) “I can safely say that nobody understands quantum mechanics” (Richard Feynman)
- 4. introduction Quantum physics is basically the recognition that there is less difference between waves and particles than was thought before. Key insights: • light can behave like a particle • particles (e.g. electrons) are indistinguishable • particles can behave like waves (or wave packets) • waves gain or lose energy only in "quantized amounts“ • detection (measurement) of a particle ⇒ wave will suddenly into a new wave • quantum mechanical interference – amplitudes add • QP is intrinsically probabilistic • what you can measure is what you can know change
- 5. electrons Tiny and very light particles Particles Negative electric charge PROPERTIES PROPERTIES Mass : 9.11 × Has spin creates 10 −31 kilograms. magnetic field Wave
- 6. electrons Electrons carry one unit of negative elementary charge. Since an electric or magnetic field exerts a force on electrons, it a ffects their motion. In spite of the fact that electric fields are everywhere around us, in every day life we do not directly observe the motion of electrons. However, such observations are possible with a device called a cathode-ray tube (CRT), which is just a technical name for a tube present in most of TV sets or computer monitors.
- 7. J.J.THOMSON’S EXPERIMENT J.J. Thomson (1856-1940) J.J. Thomson (1856-1940)
- 8. J.J.THOMSON’S EXPERIMENT J.J. Thomson was born on December 18, 1856 in Manchester. The major accomplishment of J.J. Thomson was the discovery of the electron. An electron is a particle that is smaller than an atom and is negatively charged. Thomson created the plum pudding model, which was the way he thought the structure of the atom was made up. The tiny negatively charged atoms were embedded in a positively charged cloud. (J.J. Thomsons Atom Model) (J.J. Thomsons Atom Model)
- 9. MILIKAN EXPERIMENT Robert Andrews Millikan (1868-1953) Robert Andrews Millikan (1868-1953)
- 10. MILIKAN EXPERIMENT Millikan made numerous momentous discoveries. Mainly in the fields of electricity, optics, and molecular physics. A major success was the accurate determination of the charge carried by an electron, using the elegant "falling-drop method". He also proved that this quantity was a constant for all electrons (1910), thus demonstrating the atomic structure of electricity. He verified experimentally Einstein's all-important photoelectric equation, and made the first direct photoelectric determination of Planck's constant.
- 11. MILIKAN EXPERIMENT Droplets of oil could electrify themselves owing to friction when they were atomised. They could also get the charge by X-raying. Millikan put some electric potential difference on plates generating electric field between them.
- 12. DE BROGLIE RELATION PHOTON PHOTON A particle representing a quantum of light or other electromagnetic radiation regarded as a particle with zero rest mass and charge, unit spin, and energy equal to the product of the frequency of the radiation and the Planck constant.
- 13. DE BROGLIE RELATION Prince Louis de Broglie (1892 – 1987) Prince Louis de Broglie (1892 – 1987)
- 14. DE BROGLIE RELATION In 1923, Frenchman Louis de Broglie proposed the particles of matter also had wavelengths and could behave as waves, just as photons did. He stated that under special relativity : The photon, a particle of energy, had a wavelength associated with it. The electron, particles of matter, such as electrons also had a wavelength.
- 15. DE BROGLIE RELATION Planck’s constant 6.63 x 10-34 J/s momentum mass λ = h/p = h/mv λ = h/p = h/mv velocity wavelenght de Broglie wavelength
- 16. DE BROGLIE RELATION Example: The de Broglie Wavelength of an Electron and a Baseball Determine the de Broglie wavelength of (a) an electron moving at a speed of 6.0x106 m/s and (b) a baseball (mass = 0.15 kg) moving at a speed of 13 m/s. Solution : ( 6.63 × 10 J s) = 1.2 × 10 λ = h p= ( 9.1× 10 kg )( 6.0 × 10 m s) ( 6.63 ×10 J s ) = 3.3 ×10 λ=h p= − 34 − 31 − 10 m −34 m 6 −34 ( 0.15 kg )(13 m s )
- 17. Wave particle duality HISTORY In 1927, Neils Bohr formulated his "principle of complementarity*' which In 1927, Neils Bohr formulated his "principle of complementarity*' which brought together the wave like properties of matter and the particle like brought together the wave like properties of matter and the particle like properties of light into aa coherent theoretical framework often called properties of light into coherent theoretical framework often called "wave-particle duality" or the "Copenhagen interpretation." "wave-particle duality" or the "Copenhagen interpretation."
- 18. Wave particle duality Niels Bohr (1885-1962) Niels Bohr (1885-1962)
- 19. Wave particle duality His starting point was the impossibility to distinguish satisfactorily between the actual behavior of atomic objects, and their interaction with the measuring instruments that serve to define the conditions under which the phenomena appear. Examine light with one instrument, the argument went, and it undulates like a wave; select another and it scatters like a particle. His conclusion was that evidence obtained under different experimental conditions cannot be comprehended within a single picture, but must be regarded as complementary in the sense that only the totality of the phenomenon exhausts the possible information about the objects.
- 20. Wave particle duality Wave Particle Duality Wave Particle Duality Principle of Complementarity Principle of Complementarity A system can exhibit wave-like behavior and particleA system can exhibit wave-like behavior and particlelike behavior, but no experiment could demonstrate both like behavior, but no experiment could demonstrate both behaviors simultaneously. behaviors simultaneously.
- 21. Wave NATURE OF MATTER Remember that :: Remember that Matter has dual character Matter has dual character With every body there is connected some wave. With every body there is connected some wave. The lower mass and the lower velocity the body has, the The lower mass and the lower velocity the body has, the longer is its wave. longer is its wave. Louis De Broglie created the theory of the dual nature of matter. Louis De Broglie created the theory of the dual nature of matter.
- 22. Wave NATURE OF MATTER Just as light sometimes behaves like a particle, matter sometimes behaves like a wave. The wavelength of a particle of matter is . This wavelength is extraordinarily small.
- 23. Wave NATURE OF MATTER Example: Wavelength of a ball. Calculate the de Broglie wavelength of a 0.20-kg ball moving with a speed of 15 m/s. Solution: λ = h/p = 2.2 x 10-34 m.
- 24. Wave NATURE OF MATTER Example : Wavelength of an electron. Determine the wavelength of an electron that has been accelerated through a potential difference of 100 V. Solution: The kinetic energy of the electron is classical. Its speed is found from conservation of energy: ½ mv2 = eV, so v = 5.9 x 106 m/s. The wavelength is then h/p = 1.2 x 10-10 m; roughly the size of an atom.
- 25. PLANCK’S QUANTUM HYPOTHESIS Max Karl Ernst Ludwig Planck (1858-1947) Max Karl Ernst Ludwig Planck (1858-1947)
- 26. PLANCK’S QUANTUM HYPOTHESIS He suggested that the energy of atomic oscillations within atoms cannot have an arbitrary value; it is related to the frequency: The constant h is now called Planck’s constant and n is called aa The constant h is now called Planck’s constant and n is called quantum number (discrete number) quantum number (discrete number)
- 27. PLANCK’S QUANTUM HYPOTHESIS Planck found the value of his constant by fitting blackbody curves to the formula where : I (λ , T) = radiation intensity as a function of wavelength at the temperature, T k = Boltzman’s constant c = speed of light h = Planck’s constant
- 28. PLANCK’S QUANTUM HYPOTHESIS Planck’s proposal was that the energy of an oscillation had to be an integral multiple of hf. This is called the quantization of energy. The quantum hypothesis states that the energy of an oscillator can be E = hf, or 2hf, or 3hf and so on but there cannot be vibrations with energies between these values. Energy would not be a continuous quantity.
- 29. Electron diffraction DEFINITION DEFINITION A collective scattering phenomenon with A collective scattering phenomenon with electrons electrons being being (nearly (nearly elastically) elastically) scattered by atoms in a regular array scattered by atoms in a regular array (crystal). (crystal).
- 30. Electron diffraction This can be understood in analogy to the Huygens principle for the diffraction of light. The incoming plane electron wave interacts with the atoms, and secondary waves are generated which interfere with each other. This occurs either constructively (reinforcement at certain scattering angles generating diffracted beams) or destructively (extinguishing of beams). As in X-ray diffraction (XRD), the scattering event can be described as a reflection of the beams at planes of atoms (lattice planes).
- 31. Electron diffraction The Bragg law gives the relation between interplanar distance d and The Bragg law gives the relation between interplanar distance d and diffraction angle θ: diffraction angle θ: n λ = 2 d sin θ n λ = 2 d sin θ
- 32. Electron diffraction Example : Assume that the electrons strike perpendicular to the surface of a solid, and that their energy is low, K = 100 eV, so that they interact only with the surface layer of atoms. If the smallest angle at which a diffraction maximum occurs is at 24°, what is the separation d between the atoms on the surface? Solution: The smallest angle will occur when d sin θ = λ. The electrons are not relativistic, so the wavelength can be found from the kinetic energy: λ = 0.123 nm. Then the spacing is λ/sin θ = 0.30 nm.
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Editor's Notes
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