Announcements Review: Relativistic mechanics Room: G1B30 From last class: total energy Example: Deuterium fusion Example: Deuterium fusion

Transcription

1 Announeents Review: Relativisti ehanis Reading for Monday: Chapters 1 &! Relativisti oentu: dr p propper =γ u HW 4 due Wed. Do it before the ea! a 1 in 4 days. It overs Chapters 1 &. Roo: G1B3 (net to this lassroo). Pratie ea available on CUlearn. (NOT: our ea will be all ultiple hoie) Relativisti fore: Total energy of a partile with ass : dp F = d ( γ u) tot = γ = K These definitions fulfill the oentu and energy onservation laws. And for u<< the definitions for p, F, and K ath the lassial definitions. But we found that funny stuff happens to the proper ass. Fro last lass: total energy = γ = K v v tot = K tot = M M K M > aple: Deuteriu fusion aple: Deuteriu fusion Isotopes of Hydrogen: Isotope ass: Deuteriu: u Heliu 4: u (1 u kg) 1kg of Deuteriu yields ~.994 kg of Heliu 4. nergy equivalent of 6 gras: = = (.6 kg) (3 1 8 / s ) = J nough to power ~, Aerian households for 1 year!

2 Relationship of nergy and oentu Reall: Total nergy: = γ Moentu: p = γu Therefore: p = γ u = γ 4 u / u γ 1 use: = γ p = γ 4 4 = This leads us the oentuenergy relation: or: = (p) ( ) = (p) Appliation: Massless partiles Fro the oentuenergy relation = p 4 we obtain for assless partiles (i.e. =): = p, (if =) p=γu and =γ p/u = / Using =p leads to: u=, (if =) Massless partiles travel at the speed of light!! no atter what their total energy is!! aple: letronpositron annihilation Positrons (e, aka. antieletron) have eatly the sae ass as eletrons (e ) but the opposite harge: e = e = 511 kev/ (1 ev J) Do neutrinos have a ass? Neutrinos are eleentary partiles. They oe in three flavors: eletron, uon, and tau neutrino (ν e,ν µ, ν τ ). The standard odel of partile physis predited suh partiles. The predition said that they were assless. ebam! e 1, p 1, p At rest, an eletronpositron pair has a total energy = 511 kev. One they oe lose enough to eah other, they will annihilate one other and onvert into two photons. What an you tell about those two photons? The fusion reation that takes plae in the sun (H H He) produes suh ν e. The standard solar odel predits the nuber of ν e oing fro the sun. All attepts to easure this nuber on earth revealed only about one third of the nuber predited by the standard solar odel. Do neutrinos have a ass? (ont.) Bruno Ponteorvo predited the neutrino osillation, a quantu ehanial phenoenon that allows the neutriono to hange fro one flavor to another while traveling fro the sun to the earth. Why would this iply that the neutrinos have a ass? Suary SR Classial relativity Galileo transforation Speial relativity (onsequene of '' is the sae in all inertial fraes; reeber MihelsonMorley eperient) Tie dilation & Length ontration, events in spaetie Lorentz transforation Spaetie interval (invariant under LT) Relativisti fores, oentu and energy Lot's of appliations (and lot's of firerakers) verything we have disussed to this point will be part of the first ier ea (inluding reading assignents and hoework.) If you have questions ask as early as possible!!

3 Part : Quantu* Mehanis Quantu Mehanis is the greatest intelletual aoplishent of huan rae. Carl Wiean, Nobel Laureate in Physis 1 To understand soething eans to derive it fro quantu ehanis, whih nobody understands. unknown origin Courtesy of IBM *We say soething is quantized if it an our only in ertain disrete aounts. Part of this ourse: 1. Basi properties of light (eletroagneti waves).. Photoeletri effet and how it shows light oes in quantu units of energy. When is a wave not a wave? (If it is a partile!). Atoi spetra quantized energy of eletrons in atos. 3. Bohr odel of the ato. Where it works. Why it is wrong. 4. de Broglie idea wavepartile duality of eletrons et. When is a partile not a partile? (when it s a wave). 5. Shrodinger quation and quantu waves. 6. What they are, how to use. 7. Appliations: heistry, eletronis, lasers, MRI, Rest of today (and net lass): Basi properties of light (aka. eletroagneti waves): How to generate light Wavelike properties of light Net week: Partilelike properties of light Dislaier: A very eiting part of this ourse is the partilewave duality of light (and atter!) However, do not get onfused with when to use the wave or the partile representation of the very sae physial entity. It atually depends on the eperient ( question or easureent )! We will see several eperients that should help you understand this onept. Strap in and enjoy the ride! Properties of light Interation with atter The sun produes lots of light letri fields eert fores on harges F=q _ F=q (e s and p s in ato) Fore = harge eletri field F= q Light is an osillating (and B)field. It interats with atter by eerting fores on the harges the eletrons and protons in atos. Why? How? Surfae of sun very hot! Whole bunh of free eletrons whizzing around like razy. qual nuber of protons, but heavier so oving slower, less M waves generated by protons.

4 Light is an osillating (and B)field Osillating eletri and agneti field Traveling at speed of light () Snap shot of field in tie: At t= A little later in tie a The field is a funtion of position () and tie (t): (,t) = a sin(abt) sin(abt) letroagneti radiation This sybolizes a loal disturbane of the eletri field (,t), (here: b/a=) B Reeber this one? Light soure field (for a single olor): (,t) = sin( π / ωt φ) φ = π/ω, ω = πf = π/t Wavelength of visible light is: ~ 35 n 75 n. Making sense of the Sine Wave letroagneti Spetru Spetru: All M waves. Coplete range of wavelengths. Wavelength () = distane ( ) until wave repeats Blue light Red light Cosi rays Frequeny (f) = # of ties per seond field at point hanges through oplete yle as wave passes CQ: What does the urve tell you? For Water Waves? For Sound Wave? For /M Waves? SHORT LONG letroagneti waves arry energy a =peak aplitude a (,t) = a sin(abt) X Light shines on blak tank full of water. How uh energy absorbed? Mawell s quations: Desribes M radiation Q in dφ d A= ε d s= dφe B d = B d s= µ Ithrough εµ A Intensity = Power = energy/tieα( a ) α (aplitude of wave) area area B Intensity only depends on the field aplitude but not on the olor (or frequeny) of the light!

5 Mawell s quations: Desribes M radiation Q in dφ d A= ε d s= dφ B d = B d s= µ Ithrough εµ A In 3D: 1 = t In 1D: 1 = e t How an we see that light really behaves like a wave? During 1618s: lot s of debate about what light really is. After ~1876 (Mawell): Light = M radiation viewed as a wave. How an it be tested? What is ost definitive observation we an ake that tells us soething is a wave? Show that (,t) = a os(abt) is a solution (in 1D) with b/a=. M radiation is a wave What is ost definitive observation we an ake that tells us soething is a wave? M radiation is a wave What is ost definitive observation we an ake that tells us soething is a wave? Construtive interferene: (peaks are lined up and valleys are lined up) Destrutive interferene: (peaks align with valleys fields anel eah other) Two slit interferene Light is a wave interferene! The definite hek that light IS a wave Observe interferene! wave interfarene online waveinterferene_en. waveinterferene_en.jar