The Description of the microscopic world

Transcription

1 The Description of the microscopic worl This Friay Honor lecture Previous Lecture: Quantization of light, photons Photoelectric effect Particle-Wave ualism Catherine Woowar Botany Photosynthesis This Lecture: More on Quantum mechanics Uncertainty Principle Wave functions Start the atom MTE 3 We Nov 28 5:30-7pm Ch 2103 Talk to me after this lecture an write us an if you really nee an alternate eam. Alternative possible times: We 6:30-8:00 an Thu 5:30-7:00 Contents: Ampere s Law (32.6) Faraay s Law (ch 33) Mawell equations (ch 34, no 34.2) EM waves (34.6-7) Polarization (34.8) Photoelectric effect ( ) Matter waves an De Broglie wavelength (38.4) Atom (37.6, , ) Wave function an Uncertainty (39) Quantization of light Light is mae of quanta calle photons quantum of energy: a photon carries the energy E=hf f = frequency of light Photon is a particle, but moves at spee of light Kma = hƒ This is possible because it has zero mass. Zero mass, but it oes have momentum: Photon momentum p=e/c Photoelectric effect (1905) No matter how intense is the light: until the light wavelength passes a certain threshol, no electrons are ejecte. 3 Photon Energy Quiz on photoelectric effect Which of the following is not true of photoelectric emission? A re an green laser prouce light at a power level of 2.5mW. Which one prouces more photons/secon? A. B. C. Re Green Same frequency of green light is larger than re one Re light has less energy per photon so nees more photons To etract photons from the bucket it is f that matters not how many photons 5 A. increasing the light intensity causes no change in the kinetic energy of photoelectrons B. the maimum energy of photoelectrons epens on the frequency of light illuminating the metal C. increasing the intensity of the light will increase the KE of photoelectrons D. Doubling the light intensity oubles the number of photoelectrons emitte A. is true because the intensity is connecte to the number of electrons not to the energy of each ones B. is true because Kma f C. is false because Kma epens on f D. is correct 6

2 How much is a quantum of green light? One quantum of energy for 500 nm light (green) E = hf = hc " ( ) # ( 3#10 8 m /s) #10 $34 Js = 500 #10 $9 m = 4 #10 $19 J We nee a convenient unit for such a small energy 1 electron-volt = 1 ev = charge on electron (1 volt) = J Energy of an electron accelerate in a potential ifference of 1 V In these units, E(1 green photon) = ( J)(1 ev / J) = 2.5 ev hc =1240 ev nm Swinging a penulum: the classical picture Larger, larger energy Small energy Large energy Potential Energy E=mg E.g. (1 kg)(9.8 m/s(0.2 m) ~ 2 Joules The quantum mechanics scenario Wave properties of particles Energy quantization: energy can have only certain iscrete values Energy states are separate by E = hf. f = frequency h = Planck s constant= Js Suppose the penulum has Perio = 2 sec Frequency f = 0.5 cycles/sec E min =hf= J << 2 J Quantization not noticeable at macroscopic scales e Broglie wavelength Shoul be able to see an iffraction for any material particle Wavelength of an electron of 1 ev: Solve for Result: " = 1.23 nm If m of particle is large small an wave properties not noticeable De Broglie Question Compare the wavelength of a bowling ball with the wavelength of a golf ball, if each have 10 Joules of kinetic energy. A) " bowling > " golf B) " bowling = " golf C) " bowling < " golf The largest the mass of the object the less noticeable are the quantistic effects Football launche by Brett Favre can go at 30m/s an m = 0.4kg " = h p = 6.6 #10$34 Js 0.4kg # 30m /s = 5.5 #10$35 m Davisson-Germer eperiment Diffraction of electrons from a nickel single crystal. Foun pattern by heating just by chance. Nichel forme a crystalline structure. Establishe that electrons are waves. 54 ev electrons ("=0.17nm) Bright spot: constructive Davisson: Nobel Prize 1937

3 Electron Interference an Diffraction Intensity on screen an probability of etecting electron are connecte: amount of energy in each strip D = D 1 + D 2 = Asin(kr 1 "#t) + Asin(kr 2 "#t) = = 2Acos k$r ( * sin kr [ av "#t] = 2Acos + (,L ) * sin kr Computer [ av "#t] simulation sin" + sin# = 2cos " $ # ( * sin " + # ( * $ " I() = Ccos 2 #L ( ) I " A 2 photograph Wave function When oing a light eperiment, the probability that photons fall in one of the strips aroun of with is N(in at ) Energy(in at ) /t P() = " = hf /t = I()H " A() 2 hf The probability of etecting a photon at a particular point is irectly proportional to the square of lightwave function at that point P() is calle probability ensity (measure in m -1 ) P() A() 2 A()= function of EM wave Similarly for an electron we can escribe it with a wave function () an P() () 2 is the probability H ensity of fining the electron at 14 Wave Function of a free particle #() may be a comple function or a real function, epening on the system For eample for a free particle moving along the -ais #() = Ae ik k = 2/" is the angular wave number of the wave representing the particle A is the constant Wave Function of a free particle #() must be efine at all points in space an be single-value #() must be normalize since the particle must be somewhere in the entire space Remember: comple number imaginary unit 15 The probability to fin the particle between min an ma is: P( min " " ma ) = #() 2 #() must be continuous in space There must be no iscontinuous jumps in the value of the wave function at any point $ min ma 16 Suppose an electron is a wave Analogy with soun Here is a wave: " where is the electron? " = h p Wave etens infinitely far in + an - irection Soun wave also has the same characteristics But we can often locate soun waves E.g. echoes bounce from walls. Can make a soun pulse Eample: Han clap: uration ~ 0.01 secons Spee of soun = 340 m/s Spatial etent of soun pulse = 3.4 meters. 3.4 meter long han clap travels past you at 340 m/s

4 Beat frequency: spatial localization Creating a wave packet out of many waves What oes a soun particle look like? One eample is a beat frequency between two notes Two soun waves of almost same wavelength ae. Soft Lou Soft Lou Beat 439 Hz 439 Hz Hz Constructive Large Destructive Small Constructive Large 439 Hz Hz Hz Hz A non repeating wave...like a particle Si soun waves with slightly ifferent frequencies ae together f 1 =f f 2 = f1.05 f 3 = f1.10 f 4 = f1.15 f 5 = f1.20 f 6 = f1.25 Wave now resembles a particle, but what is the frequency? Soun pulse is comprise of several frequencies The eact frequency is ineterminate, comprise in an interval f 8 Same occurs for a matter wave Construct a localize particle by aing together waves with slightly ifferent wavelengths (or frequencies). Since e Broglie says " = h /p, each of these components has slightly ifferent momentum. We say that there is some uncertainty in the momentum t J t = time uration of the pulse t ecreases as "f increases. "f # "t $1 An still on t know eact location of the particle Wave still is sprea over ( uncertainty in position) Can reuce, but at the cost of increasing the sprea in wavelength (giving a sprea in momentum). Heisenberg Uncertainty Principle = position uncertainty, p = momentum uncertainty Heisenberg showe that the prouct " = v "t = p m "t f = v # = p /m h / p = p hm $ "f = 2p "p hm Reuce Planck constant: Since E = hf it is equivalent to 2 "E # "t $ h 2 "p # " $ h 2 "f # "t = 2"p h " "f # "t $1 What s your view of atoms? Particles are waves an we can only etermine a probability that the particle is in a certain region of space. We cannot say eactly where it is 24

5 Hystory of Atoms Thompson s classical moel - raisin-cake (1897): clou of + charge with embee e - Problem: charges cannot be in equilibrium Rutherfor s eperiment (1911) $ particles Planetary moel " Positive charge concentrate in the nucleus ( m) " Electrons orbit the nucleus (r~10-10 m) Thin gol foil Problem1: emission an absorption at specific frequencies Problem2: electrons on circular orbits raiate25