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Quantum Theory, Part I The Atom Day 5
During the latter part of the 19th century and the early 20th century, while electrons and protons were being discovered, a series of experiments baffled the scientific community. These experiments proved to be inconsistent with the classical (or Newtonian)mechanics, which had worked so well for so long. (NOTE: When we talk about the motion of objects, we are usually referring to Classical Mechanics, which are the laws of motion devised by Sir Isaac Newton(Newton’s law of motion) during the seventeenth century. These laws were highly successful in explaining the observed motion of objects on the earth as well as the motions of bodies in the solar system.)
What Classical Mechanics Said: • MATTER – made up of _______ (particles) • Tiny particles are so small and close packed that objects look continuous/solid, yet there is empty space between the particles. • ENERGY – wave • Objects can have anyamount of energy! atoms
Why do we see colors? • Light of a particular wavelength is reflected into our eyes. • What happens for a whiteobject? • Light of ALL wavelengths are reflected into our eyes. • What is happening when we see black? • No light of any wavelength is reflected! • So black bodies perfectly absorb all radiation. • According to classical mechanics, if it absorbs all forms of radiation, then it must also emit all of it. • A blackbody is an object that perfectly absorbs and emits radiation.
Max Planck Blackbody Radiation Experiment (1900) • Determine the relationship between temperature & light
German physicist Max Planck studied the intensity of light of various frequencies emitted from heated solids at different temperatures. • Planck knew that the atoms of heated objects vibrated and that this vibration caused the emission of radiation. It was observed that the solid initially glows red. • As the temperature increases the red becomes mixed with more yellow and blue light, giving white light. • The color of the solid varies in a definite way with temperature. (Think about a heating coil on an electric stove.)
However, during an experiment a hot iron bar was predicted to be blue, and yet it was red. • To account for this Planck had to revise classical ideas of light being a continuous collection of EM waves to light consisting of bundles of energy. VIOLET INDIGO-VIOLET INDIGO BLUE-INDIGO BLUE GREEN-BLUE GREEN YELLOW-GREEN YELLOW ORANGE-YELLOW ORANGE RED-ORANGE RED • Planck concluded that energy can only be given off in bundles (packets) of certain energies called quanta. • The energy in each quantum influences the color of light. • In other words, for the metal to change colors, specific amounts of energy need to be absorbed or emitted. • Hence, energy is quantized.
Planck’s Conclusion: • If classical mechanics is WRONG, then ENERGY is NOT continuous (a wave), but discontinuous, made up of tiny bundles (particles) called QUANTA. • Energy is QUANTIZED (restricted to certain amounts - discontinuous) like matter. Examples: Continuous vs. Discontinuous • Ramp vs. Steps • Violin vs Piano
If a car’s velocity, if quantized if not quantized 10, 20, 30, 40, 50, 60, 70 mph10, 11, 12,…,68, 69,70 mph Violet Indigo-Violet Indigo Blue-IndigoBlueGreen-BlueGreenYellow-GreenYellowOrange-YellowOrangeRed-OrangeRed Frequency, color Energy, not quantized Planck was uneasy about this quantization assumption and tried to eliminate it from his theory
MATHEMATICALLYENERGY EQUATION: ∆E = h h (Planck’s constant) = 6.626 x 10-34 J s(0.000 000 000 000 000 000 000 000 000 000 000 6626) Units of energy can be represented Joules, J (kg . m2/s2) or erg (g . cm2/s2) ** Energy can also have the units of erg ** 1 J = 1 x 107 erg
Albert Einstein • Photoelectric Effect (1905) – prove/disprove Planck’s idea of quanta.
Acceptance of Planck’s quantum theory (quanta of energy) was slow until Albert Einstein in 1905 expanded Planck’s assumptions to include the structure of light itself. He said that light has properties of waves and of particles. This (quanta of light) was a revolutionary idea to classical physicists, and was proven with the photoelectric effect. Einstein directed monochromatic light (“laser”, Light Amplification by Stimulated Emission of Radiation) at a shiny metal surface. If the light had a high enough frequency, then electrons (called photoelectrons) would be emitted from the metal. Below this specified frequency, called the threshold frequency, no electrons would be emitted.
Photoelectric Effect • “Photo” means light and “Electric” refers to electricity. • Photoelectric effect - light of a specific / causes e-’s (photoelectrons) to be emitted from a metal surface, which are then used to complete an electrical circuit.
EXAMPLE: Sensors that operate automatic doors work based on the photoelectric effect. Light of a specific frequency causes electrons to be emitted from a metal. These electrons are then used to complete an electric circuit. When you step in front of one of these doors, you block the light from the metal, thus electrons are not emitted from it, which causes the electric circuit to not be completed. This absence of electricity causes the door to open.
Experiment #1 What Happened?? Electrons were ejected! VIOLET LIGHT 25 m/s e- e- e- METAL
Experiment #2: What happens if he increases the ? What Happened?? Same # of e’-s were ejected faster! UV LIGHT 40 m/s e- e- e- METAL
Experiment #3: What happens if he decreases the ? What Happened??NOTHING RED LIGHT METAL
Experiment #4 What is he makes it more intense = Brighter What Happened??NADA, NOTHING RED LIGHT METAL
Experiment #5: If electrons are emitted with violet light, what happens if he changes the intensity of the violet light? What Happened?? More electrons are ejected, but at the same speed! VIOLET LIGHT 25 m/s e- e- e- e- e- e- METAL
Einstein’s Conclusions: • Threshold frequency – frequency below which no electrons are emitted. Regardless of its intensity • Each metal has its own unique threshold frequency. • The higher the frequency the MORE energy the light possess and thus the FASTER the electrons are ejected. • The higher the intensity the MORE quanta (photons) are present in the light, thus the MORE electrons are ejected. • Photons of light hit surface electrons and transfer their energy • The energized electrons overcome their attraction and escape from the surface
REASONING • If quantum mechanics was TRUE, then increasing frequency, increases energy, thus the e-’s speed increases. 60J 10 J 40J 25 m/s 40 m/s light Electrons – threshold 30 J
REASONING • If quantum mechanics was TRUE, then increasing intensity, increases the # of photons, thus increasesthe # of e-’s leaving (but NOT their speed). 35 J light 25 m/s Electrons – threshold 30 J
Photoelectric Effect Illustrated If light was strictly a wave, it would not cause metals to emit electrons. This experiment thus concludes that light has particle properties. A specific quanta of energy is needed in order for the photoelectric effect to occur.
Einstein’s Contributions • Light is made up of “packets” (PARTICLES!) of energy called PHOTONS. ** Energy particles are called ______________ and light particles are called __________________. • The amount of energy a photon possesses is directly related to its NOT its intensity. Thus, Einstein proved without a doubt that classical mechanics failed when it came to objects that were very small &/or moving very fast. quanta (Planck) photon (Einstein)
COULD IT BE THAT SIMPLE?? NOPE !!
LIGHT’S DUAL NATURE Einstein applied Planck’s quantized energy to electromagnetic radiation. c = • EM radiation has: • Wave properties • Travels like a wave • 2. Particle properties • Is composed of a stream of particles called photons and If = c / E = h COMBINED EQN: Ephoton = h c DUAL-NATURE OF EM RADIATION
Einstein’s Theory of Relativity • E = mc2 • Significance is that Energy has Mass Ephoton = mc2 = h = h c / mc2 = h c / mc = h / Hence, Einstein’s theory of relativity shows that Newton’s equations do not give correct results when objects are moving at speeds close to that of the speed of light. m = h / c m = h / v v = velocity; c for light m = mass = wavelength
Another experiment could not be explained with classical physics was that of emission spectra of atoms. In 1885 Balmer, looked at an emission spectrum of hydrogen gas and he observed four well-defined lines: Wavelength (), Å Color 6563 RED 4861 BLUE-GREEN 4340 VIOLET 4102 LIGHT VIOLET There was no explanation for this according to classical mechanics, it should have been a continuum since H should possess any amount of energy.
Measured Hydrogen Spectrum The measured lines of the Balmer series of hydrogen in the nominal visible region are:
1913 - NIELS BOHR TO THE RESCUE • Planetary Atomic Model • The electron in a hydrogen atom moves around the nucleus only in certain allowed circular orbits • This model of the atom was a direct contradiction of the classical theory of motion and energy. • According to Newton, changes in kinetic energy are smooth and continuous. Yet, Bohr said that the energy of the electron could only change once it becomes “quantized.” An electron cannot exist between energy levels. • Energy levels have a definite diameter. • Using theories of classical physics and some mathematical assumptions, he calculated the radii of these allowed orbits. r = radius of e- orbitn = an integer Z = nuclear charge (atomic number) ao = Bohr radius (a constant,0.0592 nm) • Energy must be absorbed or released in order for an electron to move between energy levels. • The amount of energy released or absorbed = the difference in energy needed for an e- to be in each level.
Bohr calculated the available energy levels e- in the H atom. ()()
()() Since each element has a different number of protons in the nucleus (Z), each element’s Energy levels will have different energies, and thus are different distances apart, producing a unique line emission spectra.
At ∞, E = 0 e- no longer attracted to the nucleus n = ∞ n = 4 Energy n = 3 E = -2.42 x 10-19 J Excited State E = -5.45 x 10-19 J n = 2 Ground State n = 1 Low Energy (stable) E = -21.78 x 10-19 J Bohr’s equation can be used to calculate the energy released or absorbed for e- transitions between energy levels.
() E = negative, then energy is emitted E = positive, then energy is absorbed When energy is emitted from an electron as it moves from a higher energy level to a lower energy level, energy is released as electromagnetic radiation.
Lyman BalmerPaschen n = ∞ n = 4 n = 3 n = 2 n = 1 UV Visible Infrared
Relating to changes caused by electron transitions (solving for frequency): ()
Calculate the energy required to excite the H atom e- from n =1 to n = 6. Also, calculate the of light that must be absorbed by the e- in the ground state to reach this excited state. () Energy must be absorbed for an electron to jump from n = 1 to n = 6. Therefore, E must be positive. () • E = hc • λ • c = λν • E = hν
() () () 2 decimals • E = hc • λ • λ = hc • E
An element is heated and visible light is given off with a = 656.3 nm. What are ninitial and nfinal? 2 (Balmer series) Because light is given off, emitted, we know that nlower = () () () Too many unknowns to solve…right now • c = λν
Combining the two equations…. () () ()
ALTERNATIVE SOLUTION:An element is heated and visible light is given off with a = 656.3 nm. What are ninitial and nfinal? () Since it is visible light… () () Put that on hold for a second… • E = hc • λ But….. Is the energy + or - ?????
() ()
