Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Thermophotovoltaic wikipedia , lookup
Quantum electrodynamics wikipedia , lookup
Magnetochemistry wikipedia , lookup
Electromagnetism wikipedia , lookup
Upconverting nanoparticles wikipedia , lookup
Electromagnetic radiation wikipedia , lookup
Electromagnetic spectrum wikipedia , lookup
Atomic Physics Quantization of Energy Atomic Models Quantum Mechanics Electric and Magnetic Fields Summary • A changing magnetic field can induce a current in a circuit (Faraday’s Law of Induction) • A magnetic field is created around a current-carrying wire (Ampere’s Law) • Electric field lines start on positive charges and end at negative charges (Coulomb’s Law / Gauss’s Law) • Magnetic field lines always form closed loops with no beginning and no end (Gauss’s Law for magnetism) • These unrelated observations, experiments and equations were all known by the mid-1800s, but nothing linked them together. Maxwell’s Equations • James Clerk Maxwell (1831-1879) – Scottish theoretical physicist & mathematician • Maxwell’s Equations – Set of differential equations that describe the relationship between electric and magnetic field – Summarized all previous work of Coulomb, Ampere, Gauss, Faraday & others Maxwell’s Equations Name Differential form Integral form Gauss's law: Gauss's law for magnetism: Maxwell-Faraday equation (Faraday's law of induction): Ampère's circuital law (with Maxwell's correction): Relax!!! You don’t need to use these. Maxwell’s Equations • Predicted: – a changing magnetic field would create a changing electric field, which would, in turn, create a changing magnetic field, and so on – existence of electromagnetic waves that move through space at the speed of light – light is an electromagnetic wave • Confirmed: – Heinrich Hertz in 1887 – generated and detected the first E/M waves Electromagnetic Waves • Oscillating electric and magnetic fields • E-field and B-field are at right angles to each other • Propagates at a right angle to both fields (transverse wave) Electromagnetic Waves • EM waves can be produced most easily by an oscillating charged particle • Frequency of oscillation determines frequency of the EM wave • Wavelength related to frequency by: c/ f c 3.0 x 10 m/s 8 Electromagnetic Radiation • Energy is the ability to do work • E-fields & B-fields store energy because they exert a force (do work) on charged particles • Electromagnetic Radiation: – transfer of energy associated with electric and magnetic fields – can be transferred to objects in the EM wave’s path – can be converted to other forms, such as heat – Continuous distribution of wavelengths on the electromagnetic spectrum. Electromagnetic Spectrum Blackbody Radiation • All objects emit electromagnetic radiation – Continuous distribution of wavelengths from the infrared, visible, and UV portions of the EM spectrum – Intensity distribution of different wavelengths varies with temperature – At low temps: mostly infrared (invisible) – Temp increases: distribution shifts to visible & UV – Metals glow: red > yellow > white > blue Blackbody Radiation • Most objects absorb some incoming radiation and reflect the rest • Blackbody: – – – – Ideal system that absorbs all incoming radiation Hollow object with a small opening Perfect absorber and perfect radiator Emits radiation based only on its temperature • In 1900, Max Planck (1858-1947), proposed that the walls of a blackbody contained billions of submicroscopic electric oscillators, which he called resonators. These resonators, produced the blackbody radiation. Blackbody Radiation Classical Theory Exper. Data / Planck’s Theory as wavelength approaches zero, the amount of energy should become infinite as wavelength approaches zero, the amount of energy radiated also approaches zero energy absorbed and emitted by a single resonator is continuous energy absorbed and emitted by a single resonator occurs in certain discrete amounts Quantization of Energy • Planck found that the total energy of a resonator is an integer multiple of the frequency • Because the energy of each resonator comes in discrete units, it is said to be quantized. • Allowed energy states are called quantum states or energy levels. • Einstein applied the concept of quantized energy to light. • Photon: quantized unit of light energy • Photons are absorbed or given off by electrons “jumping” from one quantum state to another. Quantization of Energy Total Energy of a Resonator : En nhf n : quantum number; positive integer h : Planck' s constant; 6.63 x 10-34 J s Energy of a Light Quantum : (energy difference between tw o adjacent levels) E hf Measure atomic energy in electron v olts : 1 eV 1.60 x 10-19 J The Photoelectric Effect When light strikes a metal surface, the surface may emit electrons, called photoelectrons. • Classical physics predicts: – Light waves of any frequency should have enough energy to eject electrons if the intensity is high enough – At low intensities, electrons should be ejected if light shines on the metal for a long enough period of time – Increasing the intensity of the light waves should increase the kinetic energy of the photoelectrons. – Maximum kinetic energy of a photoelectron should be determined by the light’s intensity The Photoelectric Effect • Experimental evidence shows that: – No photoelectrons emitted if the light frequency falls below a certain threshold frequency, even if the intensity is very high – Threshold frequency, ft, depends on material – If light frequency exceeds ft • # of photoelectrons emitted is proportional to light intensity • Maximum kinetic energy of photoelectrons is proportional to the frequency and is independent of the intensity • Electrons are emitted instantaneously, even at low intensities • Classical physics could not explain the photoelectric effect … but Einstein could! Einstein’s Explanation • EM waves are quantized • Think of light as a stream of particles, called photons • Photon energy given by Planck’s equation • When photons collide with electrons in metal, they transfer energy to electrons E photon hf Einstein’s Explanation • If photon energy is greater than work function of the metal, photoelectrons are ejected • If photon has more energy than the work function, the difference is the kinetic energy of the photoelectrons ejected from the surface Maximum KE of Photoelectrons KEmax hf hf t KEmax : maximum KE of photoelect rons hf : energy of incoming photon hf t : work function of metal f t : threshold frequency Compton Shift • American physicist Arthur Compton (1892-1962) proposed that momentum & energy should be conserved in a collision between photons & electrons • After a collision, scattered photon should have a lower energy, therefore a lower frequency (longer wavelength) • In 1923, conducted experiments with X rays to demonstrate this change in wavelength, known as Compton shift. Models of the Atom • Thomson Model / “Plum Pudding” Model – Discovery of electron in 1897 – Negative electrons in sphere of positive charge Models of the Atom • Rutherford Model / Planetary Model – 1911 experiment by Geiger & Marsden demonstrated that practically all of atom’s mass and all positive charge must be centrally located in atom (nucleus) – Electrons orbit nucleus like planets around Sun Problems with the Rutherford Model • Electrons orbiting the nucleus would undergo centripetal acceleration • Accelerating electrons would radiate EM waves • Electrons radiating EM waves would lose energy • Loss of energy would cause electron’s orbital radius to drop • Frequency of emitted radiation would increase • Electrons would rapidly collapse into nucleus Need a better model! Atomic Spectra • • • • • Fill a glass tube with pure atomic gas Apply a high voltage between electrodes Current flows through gas & tube glows Color depends on type of gas Light emitted is composed of only certain wavelengths Atomic Spectra • Emission Spectrum: diagram or graph that indicates the wavelengths of radiant energy that a substance emits (bright lines) • Absorption Spectrum: same thing, just for light absorbed by a substance (dark lines) What does this have to do with atomic models? The Bohr Model • Similar to Rutherford’s model, but only allows certain, discrete orbits • Electrons are never found between orbits, but can “jump” from one orbit to another • Electrons only emit radiation when they jump from an outer orbit to an inner one • Energy of emitted photon is equal to energy decrease of electron. This determines frequency of emitted radiation. • Energy of emitted photon is quantized – only certain quantities are allowed. Hence, electrons undergo “quantum leaps”. (Obligatory pop culture reference) E photon Einitial E final hf Energy Levels & Emission Spectra • Lowest energy state: ground state – Radius of this state: Bohr radius – Electrons usually here at ordinary temps • How do electrons “jump” between states? – Absorb photon with energy (hf) exactly equal to energy difference between ground state & excited state – Absorbed photons account for dark lines in absorption spectrum Energy Levels & Emission Spectra • Spontaneous emission: – Electron in excited state jumps back to a lower energy level by emitting a photon – Does NOT need to jump all the way back to the ground state – Emitted photon has energy equal to energy difference between levels – Accounts for bright lines on emission spectrum – Jumps between different energy levels correspond to various spectral lines The Bohr Model Successes • Account for wavelengths of all spectral lines of hydrogen • Provides explanation for auroras • Gave expression for radius of hydrogen atom • Predicted energy levels of hydrogen • Also successful when applied to hydrogen-like atoms (only one electron) Failures • Unsuccessful when applied to multi-electron atoms • Did not explain why electrons do not radiate energy when in a stable orbit • Did not explain why other orbits do not occur • Combined classical and non-classical physics The Dual Nature of Light • Is light a particle or a wave? – Particle: blackbody radiation, photoelectric effect – Wave: interference, diffraction • Which model is correct? – Both are correct, but depends on the situation – Each phenomenon exhibits only one or the other natures of light – True nature of light is not describable in terms of a single classical idea The Dual Nature of Light Low Frequency Light (Wave Nature) • Very low energy – Difficult to detect a single photon – Photon nature of light not evident • Long wavelength – Wave effects, like diffraction and interference are easy to observe High Frequency Light (Photon Nature) • Very high energy – Easy to detect single photons – Photon nature of light is evident • Short wavelength – Wave effects, like diffraction and interference are more difficult to observe Matter Waves • Since light can be described as either a particle or a wave, can we do the same for all objects, like atoms and people and cars? • Louis de Broglie thought so! • In 1924, proposed that all matter may have wave properties and particle properties • Matter has a dual nature, just like light! • Proposed idea of matter waves Matter Waves • The larger the momentum of an object, the smaller its wavelength Matter Waves • Frequency of matter waves can be found with Planck’s equation Evidence for Matter Waves • 1927: Davisson & Germer, showed that electrons can be diffracted by a single crystal of nickel • Electron diffraction is possible because the de Broglie wavelength of an electron is approx. equal to distance between atoms (the size of the diffraction grating) • Large-scale objects don’t demonstrate this well because large momentum generates wavelengths much smaller than any possible aperture through which the object could pass (won’t be diffracted) Bohr Model Explained • De Broglie hypothesized that only certain electron orbits are stable • Circumference of orbit must contain an integral multiple of electron wavelengths • Similar to standing waves on a string The Uncertainty Principle • Wave nature of particles restricts the precision of our measurements • Werner Heisenberg (1927): – It is fundamentally impossible to make simultaneous measurements of a particle’s position and momentum with infinite accuracy – The more we learn about a particle’s momentum, the less we know of its position, and vice versa. The Uncertainty Principle: A Thought Experiment • Imagine trying to measure an electron’s position and momentum with a powerful microscope • In order to see the electron, thereby determining its location, at least one photon of light must bounce off the electron and pass through the microscope to your eye • When the photon strikes the electron, it transfers some energy & momentum to the electron. So we are less sure of the electron’s momentum. The Uncertainty Principle: A Thought Experiment Schrodinger’s Wave Equation • Erwin Schrodinger (1926) proposed a wave equation for de Broglie’s matter waves • Each particle can be represented by a wave function , , dependent on the position of the particle and time The Electron Cloud • Max Born (1926) interpreted Schrodinger’s wave function to show probability of finding an electron at certain locations • ||2 is proportional to probability of finding the electron at a certain position • Peak probability for an electron in the ground state corresponds to Bohr radius Quantum Mechanical Model • Electrons are not confined to particular orbital distances as assumed in Bohr model • Electron cloud: a probability cloud – Density at each location related to probability of finding electron at that location – Wave function predicts geometry for energy levels (some spherical, others more complex) – Most probable location still corresponds to Bohr radii, but impossible to determine actual location • Mathematical picture of the atom that explains certain aspects of atomic structure that Bohr model cannot explain