Wednesday, November 29, 2006 Modern Physics
Modern Physics Light as a Particle
Quantum Physics • Physics on a very small scale is “quantized”. • Quantized phenomena are discontinuous and discrete. • Atoms can absorb and emit energy, but the energy intervals are very tiny, and not all energy levels are “allowed” for a given atom.
Quantum physics centers on light Visible spectrum Electromagnetic spectrum
Light is a ray • We know from geometric optics that light behaves as a ray. This just means it travels in a straight line. • When we study ray optics, we ignore the nature of light, and focus on how it behaves when it hits a boundary and reflects or refracts at that boundary.
But light is also a wave! • We will study the wave nature of light in more depth later in the year. • In quantum optics, we use one equation from wave optics. • c = lf • c: 3 x 108m/s (the speed of light in a vacuum) • l: wavelength (m) (distance from crest to crest) • f: frequency (Hz or s-1)
And light behaves as a particle! • Light has a “dual nature”. • In addition to behaving as a wave, it also behaves like a particle. • It has energy and momentum, just like particles do. This particle behavior shows up under certain circumstances. • A particle of light is called a “photon”.
Calculating photon energy • The energy of a photon is calculated from it the frequency of the light. • E = hf • E: energy (J or eV) • h: Planck’s constant • 6.62510-34 J s • 4.14 10-15 eV s • f: frequency of light (s-1, Hz)
Conceptual checkpoint • Which has more energy in its photons, a very bright, powerful red laser or a small key-ring red laser? • Neither! They both have the same energy per photon. The big one has more power. • Which has more energy in its photons, a red laser or a green laser? • The green one has shorter wavelength and higher frequency. It has more energy per photon.
The “electron-volt” (eV) • The electron-volt is the most useful unit on the atomic level. • If a moving electron is stopped by 1 V of electric potential, we say it has 1 electron-volt (or 1 eV) of kinetic energy. • 1 eV = 1.60210-19 J
Sample Problem • What is the frequency and wavelength of a photon whose energy is 4.0 x 10-19J?
Sample Problem • The bonding energy of H2 is 104.2 kcal/mol. Determine the frequency and wavelength of a photon that could split one atom of H2 into two separate atoms. (1 kcal = 4186 J).
Sample Problem • How many photons are emitted per second by a He-Ne laser that emits 3.0 mW of power at a wavelength of 632.8 nm?
Wednesday, December 6, 2006 Atomic Energy Levels
Announcements • Sign in; pick up worksheet and homework score sheet • Due next Wednesday • Worksheet • Due today • Modern HW #1
less stable more stable Ionization level 0.0 eV Third excited state -1.0 eV Second excited state -3.0 eV First excited state -5.5 eV Ground state (lowest energy level) -11.5 eV Quantized atomic energy levels • This graph shows allowed quantized energy levels in a hypothetical atom. • More stable states are those in which the atom has lower energy. • The more negative the state, the more stable the atom.
Ionization level 0.0 eV Third excited state -1.0 eV Second excited state -3.0 eV First excited state -5.5 eV Ground state (lowest energy level) -11.5 eV Quantized atomic energy levels • The highest allowed energy is 0.0 eV. Above this level, the atom loses its electron. This level is called the ionizationordissociationlevel. • The lowest allowed energy is called the groundstate. This is where the atom is most stable. • States between the highest and lowest state are called excited states.
Ionization level 0.0 eV Third excited state -1.0 eV Second excited state -3.0 eV First excited state -5.5 eV Ground state (lowest energy level) -11.5 eV Quantized atomic energy levels • Transitions of the electron within the atom must occur from one allowed energy level to another. • The atom CANNOT EXIST between energy levels.
Absorption of photon by atom • When a photon of light is absorbed by an atom, it causes an increase in the energy of the atom. • The photon disappears. • The energy of the atom increases by exactly the amount of energy contained in the photon. • The photon can be absorbed ONLY if it can produce an “allowed” energy increase in the atom.
0 eV DE l -10 eV Absorption of photon by atom • When a photon is absorbed, it excites the atom to higher quantum energy state. • The increase in energy of the atom is given by DE = hf. Ground state
Absorption Spectrum • When an atom absorbs photons, it removes the photons from the white light striking the atom, resulting in dark bands in the spectrum. • Therefore, a spectrum with dark bands in it is called an absorption spectrum.
ionized 0 eV -10 eV Absorption Spectrum • Absorption spectra always involve atoms going up in energy level.
Emission of photon by atom • When a photon of light is emitted by an atom, it causes a decrease in the energy of the atom. • A photon of light is created. • The energy of the atom decreases by exactly the amount of energy contained in the photon that is emitted. • The photon can be emitted ONLY if it can produce an “allowed” energy decrease in an excited atom.
0 eV DE l -10 eV Emission of photon by atom • When a photon is emitted from an atom, the atom drops to lower quantum energy state. • The drop in energy can be computed by DE = hf. Excited state
Emission Spectrum • When an atom emits photons, it glows! The photons cause bright lines of light in a spectrum. • Therefore, a spectrum with bright bands in it is called an emission spectrum.
ionized 0 eV -10 eV Emission of photon by atom Emission spectra always involve atoms going down in energy level.
Ionization level 0.0 eV Third excited state -1.0 eV Second excited state -3.0 eV First excited state -5.5 eV Ground state (lowest energy level) -11.5 eV Sample Problem • What is the frequency and wavelength of the light that will cause the atom shown to transition from the ground state to the first excited state? • Draw the transition.
Ionization level 0.0 eV Third excited state -1.0 eV Second excited state -3.0 eV First excited state -5.5 eV Ground state (lowest energy level) -11.5 eV Sample Problem • What is the longest wavelength of light that when absorbed will cause the atom shown to ionize from the ground state? • Draw the transition.
Ionization level 0.0 eV Third excited state -1.0 eV Second excited state -3.0 eV First excited state -5.5 eV Ground state (lowest energy level) -11.5 eV Sample Problem • The atom shown is in the second excited state. What frequencies of light are seen in its emission spectrum? • Draw the transitions.
Wednesday, December 13, 2006 Photoelectric effect
Announcements • Atomic transitions worksheet is due. • Clicker quiz. • Modern Physics #2 due January 3
Remember atoms can absorb photons • We’ve seen that if you shine light on atoms, they can absorb photons and increase in energy. • The transition shown is the absorption of an 8.0 eV photon by this atom. • You can use Planck’s equation to calculate the frequency and wavelength of this photon. Ionization level 0.0 eV -4.0 eV Ground state (lowest energy level) -12.0 eV
Kinetic energy Photon energy Work function Photoelectric Effect • Some “photoactive” metals can absorb photons that not only ionize the metal, but give the electron enough kinetic energy to escape from the atom and travel away from it. • The electrons that escape are often called “photoelectrons”. • The binding energy or “work function” is the energy necessary to promote the electron to the ionization level. • The kinetic energy of the electron is the extra energy provided by the photon. e- Ionization level 0.0 eV -8.0 eV Ground state (lowest energy level) -12.0 eV
Kinetic energy Photon energy Work Function Photoelectric Effect • Photon Energy = Work Function + Kinetic Energy • hf = f + Kmax • Kmax = hf – f • Kmax: Kinetic energy of “photoelectrons” • hf: energy of the photon • f: binding energy or “work function” of the metal. e- Ionization level 0.0 eV -8.0 eV Ground state (lowest energy level) -12.0 eV
Sample problem • Suppose the maximum wavelength a photon can have and still eject an electron from a metal is 340 nm. What is the work function of the metal surface?
Sample problem • Zinc and cadmium have photoelectric work functions given by WZn = 4.33 eV and WCd = 4.22 eV. • A) If illuminated with light of the same frequency, which one gives photoelectrons with the most kinetic energy? • B) Calculate the maximum kinetic energy of photoelectrons from each surface for 275 nm light.
Question The photoelectric equation is Kmax = hf – f. Suppose you graph f on horizontal axis and Kmax on vertical. What information do you get from the slope and intercept? Slope: Planck’s Constant Intercept: -
The Photoelectric Effect experiment • The Photoelectric Effect experiment is one of the most famous experiments in modern physics. • The experiment is based on measuring the frequencies of light shining on a metal, and measuring the energy of the photoelectrons produced by seeing how much voltage is needed to stop them. • Albert Einstein won the Nobel Prize by explaining the results.
light light Photoelectric Effect experiment At voltages less negative than Vs, the photoelectrons have enough kinetic energy to reach the collector. If the potential is Vs, or more negative than Vs, the electrons don’t have enough energy to reach the collector, and the current stops. Collector (-) metal (+) e- e- e- e- e- e- e- e- e- e- e- e- e- e- e- e- e- e- e- V e- e- A e- e- e- e- e-
Experimental determination of the Kinetic Energy of a photoelectron • The kinetic energy of photoelectrons can be determined from the voltage (stopping potential) necessary to stop the electron. • If it takes 6.5 Volts to stop the electron, it has 6.5 eV of kinetic energy.
Strange results in the Photoelectric Effect experiment • Voltage necessary to stop electrons is independent of intensity (brightness) of light. It depends only on the light’s frequency (or color). • Photoelectrons are not released below a certain frequency, regardless of intensity of light. • The release of photoelectrons is instantaneous, even in very feeble light, provided the frequency is above the cutoff.
I3 I2 I1 Vs Voltage versus current for different intensities of light. Number of electrons (current) increases with brightness, but energy of electrons doesn’t! I V Vs, the voltage needed to stop the electrons, doesn’t change with light intensity. That means the kinetic energy of the electrons is independent of how bright the light is. “Stopping Potential”
f3 f2 f1 Vs,1 Vs,3 Vs,2 Voltage versus current for different frequencies of light. Energy of electrons increases as the energy of the light increases. f3 > f2 > f1 I V Vs changes with light frequency. That means the kinetic energy of the photoelectrons is dependent on light color. “Stopping Potential”
Wednesday, January 3, 2007 Photoelectric effect simulation laboratory
Announcements • Put modern physics homework #2 in folder today if you’ve got it - • extension to Friday due to holiday break. • Clicker quiz. • Simulation laboratory: lab report due next week.
slope = h (Planck’s Constant) Cut-off frequency f (binding energy) Graph of Photoelectric Equation Kmax Kmax = h f - f y = m x + b f
Photoelectric simulations • Link for simulated photoelectric effect experiment • http://lectureonline.cl.msu.edu/~mmp/kap28/PhotoEffect/photo.htm
Assignment • Run the photoelectric experiment for both metals. You must collect at least 5 data points for each metal. • Graph the data such that Planck’s constant can be determined from the slope, and the work function can be determined from the y-intercept. • Your report will consist of two data tables and two graphs, one for each metal, done in Excel. You must do a proper curve fit for your data, and clearly indicate Planck’s constant, the work function, and the cut-off frequency for each metal. • Reports are due one week from today. They may be emailed to me, or stored in the folder for your period on the N: drive. If necessary, you may print your report out and submit it as hard-copy.
Wednesday, January 10, 2007 Nuclear Decay
Announcements • Due Today: Photoelectric Excel Laboratory • Clicker quiz. • Modern #3 due next week.