Intro to Quantum Theory - Lecture Slides - Basic Concepts of Physics, Slides of Physics

Download Intro to Quantum Theory - Lecture Slides - Basic Concepts of Physics and more Slides Physics in PDF only on Docsity! Today: “Intro to Quantum Theory” (Ch.31) docsity.com A little history behind origins of quantum mechanics… • Theories on the nature of light (ca 400 BC): - Plato (and also Euclid): light = “streamers” emitted by the eye - Pythagoreans: light = fine particle emanating from luminous bodies - Empedocles: light = high-speed wave For more than 2000 years, people debated: is light a wave or particle? • Newton (1700s) – light = stream of particles (“corpuscles”); Huygens = wave theory • Young’s experiment (1800) – double-slit – showed interference of light, so concluded, light must be a wave (recall earlier, only waves interfere, particles do not). • Wave theory supported by Maxwell (light =electromagnetic wave, carrying energy), and Hertz’s demo with sparks from electric circuits • Einstein (1905): light = wave and particle! Dual nature, eg it travels with wave properties but interacts with matter as a particle would. • In fact, everything = wave and particle! • Other key figures: Planck (quanta), de Broglie and later, Schroedinger, Heisenberg docsity.com Clicker Question Which of the following is not quantized? A) Energy in a beam of laser light B) Number of people in a closed room C) Electric charge D) All are quantized E) More than one, but not all, above Answer: D For something to be quantized, means that it exists only in certain amounts – usually whole-number multiples of a certain amount (which would be the quantum for that thing). docsity.com Photon energy • Energy of a photon: E = h f • Depends on frequency, f – so a photon of higher frequency represents a higher amount of energy than a photon of lower frequency. • Note: brightness of a whole light beam depends on how many photons there are in the beam, N, whereas the energy of individual photon determined only by its frequency. i.e. energy in a beam of light is E =Nhf • E = hf gives the smallest amount of energy that can be converted to a light of frequency f N photons have energy Nhf docsity.com • So radiation of light is not continuous; rather emitted as photons with each photon “throbbing” at frequency f, carrying energy hf – i.e. radiation is quantized. • Explains why microwave radiation doesn’t cause damage to our living cells like higher-freq UV does: each photon carries too low energy. • Emission of light from atoms is quantized – so the frequencies that a type of atom fluoresces at characterizes that atom. (The electrons in an atom are arranged in quantized energy levels, and it’s the difference between these that are the frequencies seen in spectra…) • What’s the evidence for this quantization? Photoelectric effect (see shortly) Photon energy continued... docsity.com Particle nature: Photoelectric Effect • Is the effect that light incident on a metal, can eject electrons from it ! (this is used today eg. in electric eyes security devices, automatic door opening) • Instrumental in supporting quantized nature of light in 1900’s, and particle-like properties. Note that if there was no light shining on the curved plate, there would be no current. docsity.com Particle nature: Photoelectric Effect cont. • If instead, we charge the receiving plate with just enough negative charge so it repels electrons, the current can be stopped. Measure potential difference across the plates at which current is just stopped – tells you kinetic energy of the ejected electrons. • So far, said nothing that can’t be explained by wave-model of light: incident light waves can build up an electron’s vibration so much so that it breaks loose from surface. BUT there are aspects that can’t be explained from wave-nature: (next slide) docsity.com Photoelectric effect cont. • Observations that cannot be explained by wave-model of light: (1) Time-lag between turning on light and ejection of first electron is not affected by brightness or frequency of light. in dim light, wave theory would predict need more time for electron to build up enough energy to be ejected, whereas in bright light, expect it would be ejected almost immediately (2) Can observe with violet or ultraviolet light but no ejection for red light, even if intense. wave theory would predict any frequency, if intense enough can eject an electron. (3) Maximum energy of the ejected electrons is not affected by the brightness of the light. wave theory would predict brighter light with its stronger electric field, would give more energy to electrons. docsity.com Photoelectric effect cont. • So, in photoelectric effect: each electron absorbs one photon. - all or nothing effect, so no time-delay as no energy needs to build up (explains 1) - since E = hf, photon’s energy for red light is not big enough to overcome forces attracting electron to metal so it can’t be ejected. But f is greater for violet and uv, so photon gives more energy to the electron  can be ejected. (explains 2 & 4) - the brighter the light, i.e more intense, means more photons, but not more energy per photon – so more electrons get ejected but each does not get more energy (max energy of ejected electron is that of one photon, i.e. hf) (explains 3) • So photoelectric effect is conclusive proof for the particle nature of light. • But light also has wave properties – eg interference : wave-particle duality (see shortly) docsity.com Clicker Question In the photo-electric effect, is it brightness or frequency that determines the kinetic energy of the ejected electrons? How about the number of ejected electrons? A) Brightness determines both KE and number B) Brightness determines KE and frequency determines number C) Frequency determines both KE and number D) Frequency determines KE and brightness determines number Answer: D The electron’s kinetic energy depends on the frequency of the illuminating light. With high enough frequency, the # of electrons ejected is determined by the number of photons incident, ie. on the brightness. docsity.com Another Question Silver bromide (AgBr) is a light-sensitive substance used in some photographic film. Can you explain why this film may be handled without exposure in a darkroom illuminated with red light? How about blue light? How about very bright red light compared to dim blue light? (Hint: consider quantization of energy) The energy of red light is too low per photon to trigger the chemical reaction in the photographic crystals. Blue light does have enough energy. Very bright red light simply means more photons that are unable to trigger a reaction. It is safer to have bright red light than dim blue light. docsity.com Double-slit expt cont. • (Note that this and the previous slide are from Ch 29 in your book) • Extra Reading (non- examinable): What determines the spacing of the fringes? Depends on the wavelength: In the central bright fringe, paths from the two slits are the same length so waves arrive in phase ie. reinforce each other. At neighboring dark fringe, one path is longer by half-wavelength c.f. other path, so waves arrive /2 out of phase ie. cancel each other. Other bright fringes: path-lengths differ by integer x  Other dark fringes: path-lengths differ by 3/2, 5/2, 7/2 etc • This also means that red-light interference fringes (longer ) are more widely spaced than blue-light fringes. docsity.com Question (non-examinable) Would one also get a fringe pattern when light passes through 3 parallel thin slits? How about thousands of such slits? Yes! In fact an arrangement of multiple slits of identical spacings is called a diffraction grating. Through interference, diffraction gratings disperse white light into colors, like prisms do, since bright fringes of each color (ie wavelength) are at different locations. Same effect for why see pretty rainbow-like spectra from CD surfaces. “Colorful” feathers of some birds – actually tiny grooves! docsity.com Wave-Particle Duality of light • Light behaves like a wave when travelling from a source to the place where it is detected. -- cannot explain interference pattern using particles, since a stream of particles coming through each slit would come through independently of one another, striking the screen in two localized regions. No fringe pattern. • Light behaves as a particle (photon) when it is being emitted or when being absorbed at a detector e.g. photoelectric effect, or absorption by a photographic film (next slide) docsity.com The wave nature of matter is best illustrated by A)The photoelectric effect B)The double-slit experiment C) Neither Answer: B The interference pattern for an electron beam having gone through a double-slit shows that matter travels as a wave. If instead the question asked about illustrating the particle nature, the answer would be A. Clicker Question docsity.com Clicker Question If a proton and electron have identical speeds, which has a longer wavelength? A) Proton B) Electron C) Both same D) Need more information Answer: B A proton of same speed as electron has more momentum than the electron (p=momentum = mv). So, it has smaller de Broglie’s wavelength = h/p. i.e. the electron has a longer wavelength. docsity.com Uncertainty Principle • Due to Heisenberg. • Cannot simultaneously know the position x and momentum p of a quantum particle: p x > h/2   p = uncertainty in measurement of p, etc. means greater or equal to • Means that if we make a very accurate measurement of the position of a particle (small x), the uncertainty in its momentum will be very large. And vice-versa, i.e. the sharper one of these quantities is, the less sharp is the other • Other pairs of variables also have uncertainty relations, e.g. energy-time uncertainty principle: E t > h/2 docsity.com