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12 Lecture in physics. Homework wave nature of light Optical instruments Theory of Relativity Quantum Theory and Models of Atom Quantum Mechanics of Atoms Molecules and Solids Nuclear Physics and Radioactivity. Homework is due 10 December 2014. It is on the web site.
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12 Lecture in physics Homework wave nature of light Optical instruments Theory of Relativity Quantum Theory and Models of Atom Quantum Mechanics of Atoms Molecules and Solids Nuclear Physics and Radioactivity
The wave nature of light • Huygens’ principle • Interference • Thin films interference • Atmosphere light scattering • Diffraction • CD diffraction • Dispersion • Polarization
Dispersive prism In optics, a dispersive prism is a type of optical prism, usually having the shape of a geometrical triangular prism. It is the most widely known type of optical prism, although perhaps not the most common in actual use. Triangular prisms are used to disperse light, that is, to break light up into its spectral components (the colors of the rainbow). This dispersion occurs because the angle of refraction is dependent on the refractive index of a certain material which in turn is slightly dependent on the wavelength of light that is travelling through it. This means that different wavelengths of light will travel at different speeds, and so the light will disperse into the colours of the visible spectrum, with longer wavelengths (red, yellow) being refracted less than shorter wavelengths (violet, blue). This effect can also be used to measure the refractive index of the prism's material with high accuracy. In such a measurement, the prism is placed on the central rotary platform of an optical spectrometer with the incident light beam adjusted such that the refracted beam is at minimum deviation. The refractive index can then be computed using the apex angle and the angle of minimum deviation. A good mathematical description single-prism dispersion is given by Born and WolfThe case of multiple-prism dispersion is treated by Duarte. Prism dispersion played an important role in understanding the nature of light, through experiments by Sir Isaac Newton and others.
Optical instruments • Cameras • f-stop = f/D • Telescopes • Microscopes • Lenses • Normal lens • Telephoto lenses • Wide-angle lens • Zoom lens • Single-lens reflex • Circles of confusion • Depth of field • Picture sharpness
Optical instruments (continued) • Eye • Iris • pupil • Retina • Fovea • Cornea • Normal eye • Nearsightness • Farsightness • Astigmatism
Optical instruments (continued) • Underwater vision • Magnifying glass • Angular magnification • Prism • Aberrations • Chromatic aberration • Circle of least confusion • Distortion
Optical instruments (continued) • Resolution • Aperture • Rayleigh criterion • Hubble Space Telescope • Lambda limit • X-rays • Tomography • Bragg equation • Spying
Special Theory of Relativity • 1. The laws of physics have the same form in all inertial reference frames • 2. Light propagates through empty space with a definite speed c independent of the speed of the source or observer • Reference frames • Relativity principle • Ether • Length contraction • Time dilation • Twin paradox • 4-dimensional space-time
Special Theory of Relativity (continued) • Relativistic momentum • Relativistic mass • Relativistic velocities addition • GPS • E = mc2 • E2= m2c4+ p2c2
Oil-drop experiment The oil drop experiment was an experiment performed by Robert A. Millikan and Harvey Fletcher in 1909 to measure the elementary electric charge (the charge of the electron). The experiment entailed balancing the downward gravitational force with the upward drag and electric forces on tiny charged droplets of oil suspended between two metal electrodes. Since the density of the oil was known, the droplets' masses, and therefore their gravitational and buoyant forces, could be determined from their observed radii. Using a known electric field, Millikan and Fletcher could determine the charge on oil droplets in mechanical equilibrium. By repeating the experiment for many droplets, they confirmed that the charges were all multiples of some fundamental value, and calculated it to be 1.5924(17)×10−19C, within 1% of the currently accepted value of 1.602176487(40)×10−19 C. They proposed that this was the charge of a single electron.
Planck's Hypothesis In 1900 Max Planck proposed a formula for the intensity curve which did fit the experimental data quite well. He then set out to find a set of assumptions -- a model -- that would produce his formula. Instead of allowing energy to be continuously distributed among all frequencies, Planck's model required that the energy in the atomic vibrations of frequency f was some integer times a small, minimum, discrete energy, Emin = hf
Planck's Hypothesis (continued) Molecular oscillations are quantized: E=nhf, f is natural frequency of the oscillation
Black body A black body is an idealized physical body that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence. A white body is one with a "rough surface [that] reflects all incident rays completely and uniformly in all directions."
Quantum In physics, a quantum (plural: quanta) is the minimum amount of any physical entity involved in an interaction. Behind this, one finds the fundamental notion that a physical property may be "quantized," referred to as "the hypothesis of quantization". This means that the magnitude can take on only certain discrete values. A photon is a single quantum of light, and is referred to as a "light quantum". The energy of an electron bound to an atom is quantized, which results in the stability of atoms, and hence of matter in general. As incorporated into the theory of quantum mechanics, this is regarded by physicists as part of the fundamental framework for understanding and describing nature at the smallest length-scales.
Photon A photon is an elementary particle, the quantum of light and all other forms of electromagnetic radiation, and the force carrier for the electromagnetic force, even when static via virtual photons. The effects of this force are easily observable at both the microscopic and macroscopic level, because the photon has zero rest mass; this allows long distance interactions. Like all elementary particles, photons are currently best explained by quantum mechanics and exhibit wave–particle duality, exhibiting properties of both waves and particles. For example, a single photon may be refracted by a lens or exhibit wave interference with itself, but also act as a particle giving a definite result when its position is measured.
Photoelectric effect The photoelectric effect is the observation that many metals emit electrons when light shines upon them. Electrons emitted in this manner can be called photoelectrons According to classical electromagnetic theory, this effect can be attributed to the transfer of energy from the light to an electron in the metal. From this perspective, an alteration in either the amplitude or wavelength of light would induce changes in the rate of emission of electrons from the metal. Furthermore, according to this theory, a sufficiently dim light would be expected to show a lag time between the initial shining of its light and the subsequent emission of an electron. However, the experimental results did not correlate with either of the two predictions made by this theory
Compton scattering Compton scattering is the inelastic scattering of a photon by a quasi-free charged particle, usually an electron. It results in a decrease in energy (increase in wavelength) of the photon (which may be an X-ray or gamma rayphoton), called the Compton effect. Part of the energy of the photon is transferred to the recoiling electron. Inverse Compton scattering also exists, in which a charged particle transfers part of its energy to a photon.
Pair production Pair production is the creation of an elementary particle and its antiparticle, for example an electron and its antiparticle, the positron, a muon and antimuon, or a tau and antitau. Usually it occurs when a photon interacts with a nucleus, but it can be any other neutralboson, interacting with a nucleus, another boson, or itself. This is allowed, provided there is enough energy available to create the pair – at least the total rest mass energy of the two particles – and that the situation allows both energy and momentum to be conserved. However, all other conserved quantum numbers (angular momentum, electric charge, lepton number) of the produced particles must sum to zero – thus the created particles shall have opposite values of each other. For instance, if one particle has electric charge of +1 the other must have electric charge of −1, or if one particle has strangeness of +1 then another one must have strangeness of −1. The probability of pair production in photon-matter interactions increases with photon energy and also increases approximately as the square of atomic number.
Wave–particle duality Wave–particle duality is the concept that every elementary particle or quantic entity exhibits the properties of not only particles, but also waves. It addresses the inability of the classical concepts "particle" or "wave" to fully describe the behavior of quantum-scale objects. As Einstein wrote: "It seems as though we must use sometimes the one theory and sometimes the other, while at times we may use either. We are faced with a new kind of difficulty. We have two contradictory pictures of reality; separately neither of them fully explains the phenomena of light, but together they do".
Annihilation Annihilation is defined as "total destruction" or "complete obliteration" of an object; having its root in the Latin nihil (nothing). A literal translation is "to make into nothing". In physics, the word is used to denote the process that occurs when a subatomic particle collides with its respective antiparticle, such as an electron colliding with a positron, illustrated here. Since energy and momentum must be conserved, the particles are simply transformed into new particles. They do not disappear from existence. Antiparticles have exactly opposite additive quantum numbers from particles, so the sums of all quantum numbers of the original pair are zero. Hence, any set of particles may be produced whose total quantum numbers are also zero as long as conservation of energy and conservation of momentum are obeyed. When a particle and its antiparticle collide, their energy is converted into a force carrier particle, such as a gluon, W/Z force carrier particle, or a photon. These particles are afterwards transformed into other particles. During a low-energy annihilation, photon production is favored, since these particles have no mass. However, high-energy particle colliders produce annihilations where a wide variety of exotic heavy particles are created.
Complementarity In physics, complementarity is a fundamental principle of quantum mechanics, closely associated with the Copenhagen interpretation. It holds that objects have complementary properties which cannot be measured accurately at the same time. The more accurately one property is measured, the less accurately the complementary property is measured, according to the Heisenberg uncertainty principle. Further, a full description of a particular type of phenomenon can only be achieved through measurements made in each of the various possible bases — which are thus complementary. The complementarity principle was formulated by Niels Bohr, a leading founder of quantum mechanics.
Spectral line A spectral line is a dark or bright line in an otherwise uniform and continuous spectrum, resulting from a deficiency or excess of photons in a narrow frequency range, compared with the nearby frequencies. Spectral lines are often used as a sort of "atomic fingerprint," as gases emit light at very specific frequencies when exposed to electromagnetic waves, which are displayed in the form of spectral lines. These "fingerprints" can be compared to the previously collected fingerprints of elements, and are thus used to identify the molecular construct of stars and planets which would otherwise be impossible.
Bohr model In atomic physics, the Rutherford–Bohr model or Bohr model, introduced by Niels Bohr in 1913, depicts the atom as a small, positively charged nucleus surrounded by electrons that travel in circular orbits around the nucleus—similar in structure to the solar system, but with attraction provided by electrostatic forces rather than gravity. After the cubic model (1902), the plum-pudding model (1904), the Saturnian model (1904), and the Rutherford model (1911) came the Rutherford–Bohr model or just Bohr model for short (1913). The improvement to the Rutherford model is mostly a quantum physical interpretation of it. The Bohr model has been superseded, but the quantum theory remains sound.
Stationary state In quantum mechanics, a stationary state is an eigenvector of the Hamiltonian, implying the probability density associated with the wavefunction is independent of time.[1] This corresponds to a quantum state with a single definite energy (instead of a quantum superposition of different energies). It is also called energy eigenvector, energy eigenstate, energy eigenfunction, or energy eigenket. It is very similar to the concept of atomic orbital and molecular orbital in chemistry, with some slight differences
Quantum number Quantum numbers describe values of conserved quantities in the dynamics of a quantum system. In the case of quantum numbers of electrons, they can be defined as "The sets of numerical values which give acceptable solutions to the Schrödinger wave equation for the Hydrogenatom". Perhaps the most important aspect of quantum mechanics is the quantization of observable quantities, since quantum numbers are discrete sets of integers or half-integers, although they could approach infinity in some cases. This is distinguished from classical mechanics where the values can range continuously. Quantum numbers often describe specifically the energy levels of electrons in atoms, but other possibilities include angular momentum, spin, etc. Any quantum system can have one or more quantum numbers; it is thus difficult to list all possible quantum numbers.
Ground state The ground state of a quantum mechanical system is its lowest-energystate; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than the ground state. The ground state of a quantum field theory is usually called the vacuum state or the vacuum. If more than one ground state exists, they are said to be degenerate. Many systems have degenerate ground states. Degeneracy occurs whenever there exists a unitary operator which acts non-trivially on a ground state and commutes with the Hamiltonian of the system. According to the third law of thermodynamics, a system at absolute zerotemperature exists in its ground state; thus, its entropy is determined by the degeneracy of the ground state. Many systems, such as a perfect crystal lattice, have a unique ground state and therefore have zero entropy at absolute zero. It is also possible for the highest excited state to have absolute zerotemperature for systems that exhibit negative temperature.
Excited state Excitation is an elevation in energy level above an arbitrary baseline energy state. In physics there is a specific technical definition for energy level which is often associated with an atom being excited to an excited state. In quantum mechanics an excited state of a system (such as an atom, molecule or nucleus) is any quantum state of the system that has a higher energy than the ground state (that is, more energy than the absolute minimum). The temperature of a group of particles is indicative of the level of excitation (with the notable exception of systems that exhibit Negative temperature). The lifetime of a system in an excited state is usually short: spontaneous or induced emission of a quantum of energy (such as a photon or a phonon) usually occurs shortly after the system is promoted to the excited state, returning the system to a state with lower energy (a less excited state or the ground state). This return to a lower energy level is often loosely described as decay and is the inverse of excitation.
Matter wave All matter can exhibit wave-like behaviour. For example a beam of electrons can be diffracted just like a beam of light or a water wave. Matter waves are a central part of the theory of quantum mechanics, an example of wave–particle duality. The concept that matter behaves like a wave is also referred to as the de Broglie hypothesis (/dəˈbrɔɪ/) due to having been proposed by Louis de Broglie in 1924. Matter waves are often referred to as de Broglie waves.
Balmer series • Lyman series • Paschen series
Photosynthesis chemical equation 6CO2 + 6H2O ------> C6H12O6 + 6O2 Sunlight energy Where: CO2 = carbon dioxideH2O = waterLight energy is requiredC6H12O6 = glucoseO2 = oxygen
de Broglie wave length λ = h/p
Compton effect λ' = λ + (1 – cosA)h/(mc)
Exercises • 41. The Sun’s surface temperature: Estimate the surface temperature of our Sun, given that the Sun emits light whose peak intensity occurs in the visible spectrum at around 500 nm. • 42. Star color: Suppose a star has a surface temperature of 32,500 K. What color would this star appear? • 43. Calculate the energy of a photon of blue light (λ = 450 nm) in the air or in vacuum.
Exercises (continued) • 44. Estimate how many visible light photons a 100-W light bulb emits per second. The efficiency of the bulb is 3%, the rest of the energy goes to heat. • 45. Photon momentum and force: 1019 photons emitted per second from 100-W light bulb are focused on the peace of black paper and absorbed. Calculate the momentum of one photon and estimate the force all these photons can exert on the paper.
