Be Name Modern Photoelectric Effect Teacher Period objects produce electromagnetic raciation in the visible region, Objects have to be about 1000 K to emit radiation in the visible range. Then they glow “red hot’ (Like the heating coil on an electric stove) As the temperature increases, the frequency ofthe emitted radiation increased, thus the wavelength decreases, 6000 K Intensity e — Al the same time, others were trying to explain bright line spectra. Every element has its own Mrerssion spectrum, 80 the explanation must have something to do withthe atone stuctarn More on this later. 1887 — Hertz discovered the photoelectric effect. Tneoming——> radiationKey findings forthe photoelectric effect ( A threshold frequency, fo, exists * There is no “lag time” — an electron cannot sit and "soak-up" wave after wave of energy and then leave when it accumulates enough energy. * The maximum kinetic energy of the emitted photoelectron is proportional to the frequency of the incident radiation, + The maximum kinetic energy of the emitted photoelectron is independent of the intensity of the incident radiation. * The current of emitted photoelectrons is proportional to the intensity of the incident radiation To measure the maximum kinetic energy of the photoelectron. Incoming-——> radiation + Hook the battery in backwards. Use an incoming radiation that has a frequency greater than the threshold frequency. + Increase the potential difference between the plates (use a variable source of emf) until the current Stops, This iS Vaop (the stopping potential) + Thework done by the electric field is equal to the change in the kinetic energy of the electron. W=AK andW=qv Weep = Kes Einstein's explanation won him the Nobel Prize in 1905: | Kroc hf-® where the energy of the incoming photon the work function = the energy an electron uses to break free of the metal 80: Kroc * En — Evo in west -nw iitef. i + The current is proportional to the intensity more current. |= Qt, 8x 10" Joules 1ev= the threshold frequency for each metal, Ke Metal 1 Metal 2 frequency .73 eV, find the threshold frequer he information fre ey is 8x 10" Ha’ these is greater than the threshold frequency, more electrone/seeorid cen be emitted, Hence, for a Silver Surface [C8J 5" ed. p. 894) * [2/8 Proportional to the maximum kinetic energy ofthe elect: Each photon hee energy equal to 's used as kinetic energy for the photoelectron, ; More intense means more photons. If the frequency of He: @ Is often glven in eV and must be changed to joules to use in the equations. ‘IF you plot Knox Vs. frequency, the lines for each metal are parallel and the slope is “h". The x intercept is “Metal ¢ncy and the threshold wavelength for the substance.‘AP-B Photoelectric Problem [8200587 modified — removed part d] ( ‘ja monochromatic source emits a 2.5 mW beam of light of wavelength 450 nm. (a) Calculate the energy of a photon in the beam. (b) Calculate the number of photons emitted by the source in 5 minutes. ‘The beam is incident on the surface of a metal in a photoelectric-effect experiment. The stopping potential for the emitted electron is measured to be 0.86 V. (c) Calculate the maximum speed of the emitted efectrons.Re Name ; % Modern Treacher = i SS 0: i Bright Line Spectrum Petod Models of the Atoms Plum Pudding Model - J.J. Thomson (discovers the electron in 1897) ¢ Hf you're not familiar with plum pudling think ofthe atom as a chocolate chip cookie. ‘+ Atom is electrically neutral, * The positive material is the pudding or cookie. 7 * The negative material is the plums or chocolate chips. | Planetary Model - Ernest Rutherford (discovers the proton in 1919) Description Nucleus at the center (ike the sun) Nucleus contains all the positive charge Electrons in circular orbits around nucleus (like the planets) Electrons contain all the negative charge riment ~ Gold Foil Experimental Results 3 Some « deflected through large angles. - Indications ofa large positive charge. * Some a bounced back. - Indications of a dense nucleus. ms | Rutherfore’s model didn't explain atomic absorption & emission spectrum, Another issue: Electrons in circular orbits * Must experience centripetal acceleration + Accelerated charges emit radiation * Radiation is energy * So electrons must lose energy over time .; Eventually electrons should fall into nucleus this model predicted an unstable atom rption or emission of photonic energy. ‘ontinuous - Produced by a glowing hot solid, ht-Line or Emission - Produced by a hot gas Fictine or Absorption - Produced by a cool gas intervening between the observer and a hot solid Pectrum is a “photo-negative" of the emission spectrum 2268) appear in precisely the same location as corrcoponding bright nos from the. Pectrum of the same gasBohr Model (1913) Description ‘+ The electrons only move in “stationary orbits”, Only certain orbits are stable (50 only certain orbits are "permitted’), {In these orbits, electrons do not emit radiation, Electrons can move “up” and “down” between orbits He didn't say how it was possible! + Based his postulates on evidence from absorption and emission spectra Spectral Lines a ‘Transition (Jumping) Rules : 4. Radiation is absorbed when an electron jumps "up" from a lower orbit to a higher orbit. 2. Radiation is emitted whan an electron falls “down” from a higher orbit to a lower orbit 3a tesons can only jump between orbits (energy levels), can’t land in between (quantum idea) ‘Transitions and Bright-Line Spectra Electrons falling toward nucleus require a photon to be emitted - Explains BrightLine spectra, Transitions and Dark-Line Spectra Electrons jumping away from nucleus require a photon to be absorbed - Explains Dark-Line spectra Mathematical Description ‘= Recall that spectra are unique. ‘Spectra are the result of electron transitions between energylorbital levels. Energy/orbital levels are unique Nucleus has positive charge, and electrons have negative charge. ‘The bound electrons have negative energy compared to free electrons. Eneray Levels and Energy Level Number ‘+ Energy levels are negative. - Negative electric potential energy. ‘+ ‘nis Bohr's principle quantum number or energy level number. ‘+ Numbered from nucleus outward. Ground State ‘+ Lowest (deepest) energy level + Closest to the nucleus, Excited State + Elevated to an energy level above ground state, + Moved away from the nucleus.bots stat withthe simplest atom — hydrogen. it has one eleciton and one proton, ‘The magnitudes of the energy levels were determined (read C8 5" ed, P. 952-83 for the gory details, From this we can draw an energy level diagram for hydrogen 0.54 eV Ec hisey i Be sey Ep 34ev mel ——$———— Be136 6 E, 3 lowest energy level an electron can occupy ie called the ground stato. All other energy levels are “excited states" ~ it took energy to gat there. 13.6 €V/n* This formula works only for hydrogen. higher energy level requires energy to be absorbed, A transition to a ‘ower level requires energy to be emitted, 1 AE\s the diference in energy between two energy levels, iven off or absorbed 4 are called the Lyman series (think of L = 4 on an old typewriter) 2 are called the Balmer series (B is the 2” letter of the alphabet) 3 Org called the Paschen series (3 isa triangle ~ passionate) 4 are called the Brackett series, = 9 are called the Pfund series, Oniy the Balmer series is in the visible range xa - ih, noves from energy level 5 to energy level 4in a hydrogen atom. Determine the energy, Sth, and the frequency of the emitted photon, AE = -‘The Bohr model has one major disadvantage ~ it only works for one-electron atoms. H, He", Li { For other atoms it is necessary fo use a quantum mechanical approach. In order to establish his energy levels, Sohr assumed that angular momentum was quantized and came in bundles of h/2rr. This led to his equation mvr = h/2rr. De Broglie got the same result by thinking about standing waves. He said that acceptable radii were those where the circumference of the orbit was a whole number muttiple of the wavelength of the electron. 2ne=nh but A= hip 2nr = nhip When we start working at a level where we are calculating the energy of photons, there is one other idea |we need to explore — the Heisenberg Uncertainty Principle (1925). It states that itis impossible to know simultaneously measure both the position and momentum of an object h poaytnien2 “pena ARDp =H Of course in 1926 Erwin Schrodinger comes up with an answer to the Uncertainty Principle. He develops the concept of mathematically locating the electron based upon the probability of finding an electron in a region of space. He kept the idea of quantized energy levels and said there were a finite number of solutions to the problem. You might recall the electron orbitals from chemistry, s-p-def. a