From Last Time. Summary of Photoelectric effect. Photon properties of light
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1 Exam 3 is Tuesday Nov. 25 5:30-7 pm, 203 Ch (here) Students w / scheduled academic conflict please stay after class Tues. Nov. 8 (TODAY) to arrange alternate time. From Last Time Photoelectric effect and light quantization Covers: all material since exam 2. Bring: Calculator One (double-sided) 8 /2 x note sheet Exam review: Thursday, Nov. 20, in class 2 Summary of Photoelectric effect Light comes in photons - particles of light = hf = hc /" h=planck s constant Red photon is low frequency, low energy. (Ultra)violet is high frequency, high energy. Electron in metal absorbs one photon Can escape metal if photon energy large enough >Work function E o Excess energy -E o shows up as kinetic energy properties of light of frequency f has energy hf Red light made of ONLY red photons = hf = hc /" h = "0 #34 J s = 4.4 "0 #5 ev s hc =240eV " nm The intensity of the beam can be increased by increasing the number of photons/second. s/second = energy/second = power 3 4 How many photons can you see? In a test of eye sensitivity, experimenters used milli-second (0.00 s) flashes of green light. The lowest power light that could be seen was 4x0-4 Watt. How many green (500 nm, 2.5 ev) photons is this? A. 0 photons B. 00 photons C.,000 photons D. 0,000 photons ( 4 "0 #4 J /s)( 0.00s) = 4 "0 #7 J ( 4 "0 #7 J) ( ev /.6 "0 #9 J) = 250eV ( 250eV )( photon /2.5eV ) =00 photons Quantization of light Quantum mechanically, brightness can only be changed in steps, with energy differences of hf. Possible energies for green light (λ=500 nm) One quantum of energy: one photon Two quanta of energy two photons etc Think about light as a particle rather than wave. E=4hf E=3hf E=2hf E=hf Energy 5 6
2 Thompson s model of atom J.J. Thomson s model of atom A volume of positive charge Electrons embedded throughout the volume A change from Newton s model of the atom as a tiny, hard, indestructible sphere This model is not correct! 7 8 Resulted in new model Planetary model Based on results of thin foil experiments Positive charge is concentrated in the center of the atom, called the nucleus Electrons orbit the nucleus like planets orbit the sun Difference between atoms Simplest is Hydrogen: electron orbiting proton Other atoms number of orbiting negative electrons same as number of positive protons in nucleus Different elements have different number of orbiting electrons Helium: 2 electrons Copper: 29 electrons Uranium: 92 electrons! Organized into periodic table of elements First concentrate on hydrogen atom 9 0 Circular motion of orbiting electrons: electrons emit EM radiation at orbital frequency. Similar to radio waves emitted by accelerating electrons in a antenna. In an atom, emitted EM wave carries away energy Planetary model and radiation Electron predicted to continually lose energy. The electron would eventually spiral into the nucleus However most atoms are stable! Line spectra from atoms Atoms do emit radiation, but only at certain discrete frequencies. Emission pattern unique to different atoms Spectrum is an atomic fingerprint, used to identify atoms (e.g. in space). Hydrogen Mercury Wavelength (nm) 2 2
3 The Bohr atom Retained planetary picture with circular orbits Only certain orbits are stable Radiation emitted only when electron jumps from one stable orbit to another. E initial E final Energy levels Instead of drawing orbits, just indicate energy an electron would have if it were in that orbit. Here, the emitted photon has an energy of E initial -E final Stable orbit Stable orbit Energy axis 3 4 Hydrogen atom energies Quantized energy levels: Each corresponds to different Orbit radius Velocity Particle wavefunction Energy Each described by a quantum number n E n = " 3.6 n 2 ev Energy 5 emitted Emitting and absorbing light is emitted when electron drops from one quantum state to another absorbed Absorbing a photon of correct energy makes electron jump to higher quantum state. 6 Hydrogen emission This says hydrogen emits only photons of a particular wavelength, frequency Hydrogen atom An electron drops from an -.5 ev energy level to one with energy of -3.4 ev. What is the wavelength of the photon emitted? energy = hf, so this means a particular energy. Conservation of energy: Energy carried away by photon is lost by the orbiting electron. A. 827 nm B. 653 nm C. 476 nm D. 365 nm E. 243 nm emitted hf = hc/λ = 240 ev-nm/ λ E 3 = ".5 ev E 2 = "3.4 ev E = "3.6 ev 7 8 3
4 Energy conservation for Bohr atom Each orbit has a specific energy E n =-3.6/n 2 emitted when electron jumps from high energy to low energy orbit. E i E f = h f absorption induces electron jump from low to high energy orbit. E f E i = h f Agrees with experiment! Hydrogen emission spectrum Hydrogen is simplest atom One electron orbiting around one proton. The Balmer Series of emission lines given empirically = R H " m 2 # ' & ) 2 n 2 R ( H =0.0097nm - n = 4, λ = 486. nm Hydrogen n = 3, λ = nm 9 20 Balmer series Transitions terminate at Each energy level has energy E n =-3.6 / n 2 ev E.g. n to 2 transition Emitted photon has energy ## = " 3.6eV & # ( " " 3.6eV && ( n 2 ' 2 2 '' ( =3.6 ev # 2 " & 2 n ( 2 ' Emitted wavelength " = hc 240 ev # nm = 3.6 ev 2 # ' & ) 2 n 2 ( # = 9.8nm /2 2 #/n 2 ( ) Why stable orbits? Bohr argued that the stable orbits are those for which the electron s orbital angular momentum L is quantized as L = m e v r = n h Electron velocity Electron orbit radius Integer:,2,3 # h = h & ( 2" ' Bohr combined this with the Coulomb force to find allowed orbital radii and energies Including more physics Bohr model of H-atom Circular orbit, electron is accelerating (centripetal acceleration = v 2 /r = Force/mass) Force causing this accel. is Coulomb force ke 2 /r 2 between pos. nucleus and neg. electron v 2 r = F Coulomb m Also gives a condition for angular momentum. Orbital motion: p = mv Quantization: v 2 r centripetal acceleration = F Coulomb /m = k e2 r 2 /m Coulomb force / mass ( mv r) 2 = L 2 = mke 2 r L 2 = ( mvr) 2 = n 2 h
5 Radius of H-atom states Energy of H-atom states L 2 = n 2 h 2 and L 2 = mke 2 r Quantization Quantized orbital radius n a o 2 4a o 3 9a o orbit radius n 2 h 2 = mke 2 r " r = n 2 h 2 # mke 2 ' = n 2 a o & a o = Bohr radius " 0.529Å Total Energy = kinetic + potential " p 2 " r ' + (k e2 n = n 2 a o ' # 2m& # r & " " k e2 ' + (k e2 ' = ( k e2 # 2r& # r & 2r = ( " ke2 ' # 2a o & n 2 ( )(.6 "0 9 C) 2 ( ) ke 2 = 9 "0 9 N # m 2 /C 2 2a o "0 0 m = 2.8 "0 8 J Quantized energy 3.6 ev E n = " n Energy quantization in a pendulum Swinging pendulum. Larger amplitude, larger energy Energy quantization Energy can have only certain discrete values Energy states are separated by ΔE = hf. ΔE = hf=3.3x0-34 J for pendulum f = frequency = spacing between energy levels h = Planck s constant= x 0-34 J-s Small energy Large energy Quantum mechanics: Not every swing amplitude is possible energy cannot change by arbitrarily small steps d Suppose the pendulum has Period = 2 sec Freq = 0.5 cycles/sec E=mgd=( kg)(9.8 m/s 2 )(0.2 m) ~ 2 Joules ΔE min =hf=3.3x0-34 J << 2 J Quantization not noticeable Question This quantum system has equally-spaced energy levels as shown. Which photon could possibly be absorbed by this system? = hc 240 ev # nm = " " E 3 =7 ev E 3 =5 ev A. 240 nm B. 43 nm C. 30 nm D. 248 nm E 2 =3 ev E = ev 29 5
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