Today Announcements: HW#7 is due after Spring Break on Wednesday Marc 1 t Exam # is on Tursday after Spring Break Te fourt extra credit project will be a super bonus points project. Tis extra credit can let your omework score go over 0% Ligt Wave-particle duality of nature Quantum Mecanics Te Electromagnetic Spectrum Maxwell s 4 equations describe te unity of electric and magnetic forces. Tey predict an electromagnetic wave tat travels at te speed of c (3.00E+8 m/s) ISP09s8 Lecture 14-1- ISP09s8 Lecture 14 -- Wavelengt and Frequency Te Electromagnetic Spectrum λ 1.0 m period.0 s Speed λ f λ wavelengt f Frequency, Hz (1/period)(1/s) For ligt Speed c 3.0E+8m/s Wavelengt Frequency 1/period Distance over wic te wave repeats Number of cycles (repeats) per second. ISP09s8 Lecture 14-3- Prentice-Hall 005 ISP09s8 Lecture 14-4-
Wat is Ligt? Wave Picture oscillating electric and magnetic fields Waves can interfere Examples -slit interference diffraction diffraction -slit interference Ligt as a particle Ligt also beaves like a particle Ligt comes in small bundles of energy we call potons Energy (of a poton) f 6.65E-34 Js 4.136E-15 evs ISP09s8 Lecture 14-5- ISP09s8 Lecture 14-6- Around Visible Electromagnetic Spectrum Explanation of Electric Forces and Gravity Coulomb s Law (Electric Force) kq q F 1 ; k 8.99E + 9 Nm r Coulomb force is carried by potons Newton s Universal Law of Gravity: Gm m F r 1 ; G 6.673E 11 Gravity is carried by te graviton. Nm C kg ISP09s8 Lecture 14-7- ISP09s8 Lecture 14-8-
intensity Wy is tere always r? I ate r. Inverse square law L[Watts] d L is te luminosity(measured in watts), d is te distance to te source Tis explains wy te electric force as te form it does. Te strengt of te force is related to te probability of being it by a poton. Tat decreases as te square of te distance. ISP09s8 Lecture 14-9- Feynman Diagrams Feynman Diagrams are a pictorial way of writing te interaction between two particles. Example: Two electrons interacting by te Coulomb force time space A line tat begins and ends in a diagram corresponds to a virtual particle. Oters are real particles. ISP09s8 Lecture 14 -- How do we know about potons? Atomic Spectra Atoms and molecules exists fixed states of energy Emission Transition Excited state 3.0 ev 0 ev Absorption Ground state Energy of poton E i E f 3.0 0 3.0 ev If te electron is completely removed, tis is called ionization. ISP09s8 Lecture 14-11- ISP09s8 Lecture 14-1-
An even bigger surprise! Particles like electrons also beave like waves! Example Demo: electron diffraction de Broglie wavelengt of a particle ( is Plank s constant) λ ; p 6.65 J s Wat is te wave lengt an electron wit an energy of 30 kev? λ p m E 19 e 31 9.11 λ 7.084 6.65 Js 00eV 1.6 kg 30keV kev ev 1 m ISP09s8 Lecture 14-13- J Wat is waving? Probability all particles are caracterized by a wave function. Te square of te wave functions give te probability density of finding a particle per unit volume. Te wave function extends over all space. Te square of te wave function times a volume give te probability of finding te particle in tat volume. Tis is te picture of Erwin Scrödinger: Matter is defined by te evolution in time of a wave function. HΨ EΨ Ψ wave function ISP09s8 Lecture 14-14- Bosons and Fermions Particles come in two types Bosons ave te property tat tey can overlap. Examples are potons and certain atoms (elium) Fermions can not exist in te same state. Examples electrons, protons. Te fermion nature of elections explains atomic structure ISP09s8 Lecture 14-15- Old picture - + Electron Wave functions in atoms New Picture: Examples of wave functions Te nucleus sits at te center and tese picture sow possible regions were te electrons migt be. ISP09s8 Lecture 14-16-
Heisenberg s Uncertainty Principle Uncertainty depends on mass If a particle as a wavelengt, its position and speed are not perfectly defined. Uncertainty Principle: It is not possible to know exactly te position and momentum of a particle at te same time. ΔxΔp Tere is no absolute knowledge. Te Newtonian view of te world (if everyting were known, everyting could be predicted) in not attainable. momentum proton electron baseball, igly exaggerated (by 5 ) position ISP09s8 Lecture 14-17- ISP09s8 Lecture 14-18- Tere are two versions ΔxΔp Sample Problem ΔEΔt If te position of a proton, mass 1.67E-7 kg, is known to 1E-9 m te momentum and velocity could ave a range of 6.65 Js 6 Δp 5.7 kg m 9 Δx 1.00 m s 6 Δp mδv 5.7 kg m s 6 5.7 kg m Δv s 31.6 m 7 1.67 kg s ISP09s8 Lecture 14-19- Summary Nature is governed by te rules of probability. No one can predict te exact outcome of a measurement. All knowledge is imperfect. Tere is no absolute knowledge of te position and velocity of objects. ISP09s8 Lecture 14-0-