Early Quantum Theory AP Physics Chapter 27

Early Quantum Theory 27.1 Discovery and Properties of the Electron

Glass tube filled with a small amount of gas When a large voltage was applied A dark shape seemed to extend from the cathode 27.1

27.1 Discovery and Properties of the Electron Name Cathode Rays Deflected by electric or magnetic fields Negative charge JJ Thompson – discovered the electron Believed that the electron was a part of the atom Robert Millikan – determined the charge on an electron 27.1 Experiment Video

Early Quantum Theory 27.2 Planck’s Quantum Hypothesis

Blackbody Radiation – all objects emit radiation proportional to T 4 (in Kelvin) Normal Temp – low intensity Above 300K – we can sense the IR as heat At about 1000K objects glow Above 2000K glow yellow -white 27.2

27.2 Planck’s Quantum Hypothesis As temperature increases EMR emitted increases increases toward higher frequencies 27.2

27.2 Planck’s Quantum Hypothesis Blackbody – absorbs all the radiation that falls on it Blackbody radiation – the EMR that a blackbody emits when hot and lumnous Max Plank (1900) – purposed his Quantum Hypothesis Energy of any molecular vibration could only be a whole number multiple of a minimum value 27.2

27.2 Planck’s Quantum Hypothesis h is called Planck’s constant Since energy has to be a whole number multiple n – is a quantum number It is quantized – occurs in only discrete quantities 27.2

Early Quantum Theory 27.3 Photon Theory of Light and the Photoelectric Effect

27.3 Photon Theory of Light Einstein (1905) – when an object emits light its energy must be decreased by hf, so light is emitted in quanta where Where f is the frequency of the quanta emitted Light is transmitted as tiny particles called photons 27.3

27.3 Photon Theory of Light When light shines on metals – electrons are emitted from the surface Called the photoelectric effect Both photon theory and wave theory are consistent with this basic result 27.3

27.3 Photon Theory of Light Wave theory predicts (for monochromatic light) 1.Increased light intensity should a. Increase the number of electrons ejected b. The maximum kinetic energy of the should be higher 2. Frequency of light should not affect kinetic energy, only the intensity 27.3

27.3 Photon Theory of Light Photon theory predicts (for monochromatic light) All photons of the same frequency would have the same energy All the energy of a photon would be transferred to an electron Since electrons are held in the metal by some force, a minimum energy must be reached before an electron can be emitted 27.3

27.3 Photon Theory of Light Photon theory predicts (for monochromatic light) This minimum energy is called the work function (W 0 ) Electrons that absorb less than W0 will not be ejected Those that are ejected the energy will be For the least tightly held electrons 27.3

27.3 Photon Theory of Light Photon theory predicts (for monochromatic light) 1.Increase in intensity will result in a. More electrons being ejected b. The same maximum kinetic energy for all the electrons 2. If frequency is increased, the maximum kinetic energy increase linearly 27.3

27.3 Photon Theory of Light Photon theory predicts (for monochromatic light) 3.Below a cutoff frequency no electrons will be ejected Experiments have proven that emitted electrons follow the photon theory 27.3

Early Quantum Theory 27.4 Energy, Mass, and Momentum of a Photon

27.4 Mass, Energy, and Momentum of a Photon The momentum of a particle at rest is given by (from relativity chapter) Since a photon travels a c, either it has infinite momentum, or its rest mass is 0 (makes sense, the photon is never at rest) The energy of a photon is 27.4

27.4 Mass, Energy, and Momentum of a Photon The momentum of a photon is developed from the relativistic formula Since m 0 =0 Usually written 27.4

Early Quantum Theory 27.6 Photon Interactions; Pair Production

27.6 Photon Interaction, Pair Production Four interactions that photons undergo atoms 1.Photoelectric effect 2.Move an electron to an excited state 3.Photon can be scattered resulting in lower frequency (energy) photon – called the Compton Effect 27.6

27.6 Photon Interaction, Pair Production Four interactions that photons undergo atoms 4.Pair production – a photon creates matter The photon disappears and produces a electron-positron pair Example of mass being produced in accord with The positron will quickly collide with an electron 27.6

27.6 Photon Interaction, Pair Production Pair production must occur near a nucleus so that momentum can be conserved Used in PET scanners (positron emission tomography) 27.6

Early Quantum Theory 27.7 Wave-Particle Duality

Light properties can sometimes only be explained using particle theory (photons) Sometimes the properties can only be explained using wave theory. This realization that light has both properties is called wave-particle duality The principle of complementarity – to fully understand light, we must be aware of both its particle and its wave natures 27.7

Early Quantum Theory 27.8 Wave Nature of Light

27.8 Wave Nature of Matter Louis de Broglie (1923) – proposed all particles have wave properties The wavelength of a particle is related to is momentum This is called the de Broglie wavelength 27.8

27.8 Wave Nature of Matter The wavelength of a 0.20kg ball traveling at 15 m/s would be This is ridiculously small Interference and diffraction only occur if a slit is not much larger than the wavelength So the wave properties of ordinary objects is not detectable 27.8

27.8 Wave Nature of Matter But atomic particles have small enough masses that their de Broglie wavelength is measureable This is the diffraction pattern of an electron 27.8

Early Quantum Theory Early Models of the Atom

Plum Pudding Model (1890) JJ Thomson – homogeneous sphere of positive charge embedded with negative electrons 27.10

27.10 Early Models of the Atom Planetary Model (1911) Ernest Rutherford Tiny positively charged nucleus contains most of the mass Electrons orbit around the nucleus like planets around the sun 27.10

Early Quantum Theory Atomic Spectra: key to the Structure of the Atom

27.11 Atomic Spectra If a pure gas in a tube is excited It produces a discrete spectrum When looked at through a spectrometer we can observe a emission spectrum unique to that element If a continuous spectrum passes through a gas, dark lines, or an absorption spectrum, is visible 27.11

27.11 Atomic Spectra It is assumed that in low density gases, the spectrum is from individual atoms Hydrogen is the simplest atom, and shows a regular pattern to its spectral lines JJ Balmer – showed that four lines in the visible spectrum of hydrogen have wavelength that fit the formula 27.11

27.11 Atomic Spectra R is called the Rydberg Constant n = the integer values starting with 3 Later, the Lyman series was found to fit Paschen series 27.11

Early Quantum Theory The Bohr Model

27.12 Bohr Model Niels Bohr – electrons cannot lose energy continuously, but in quantum jumps Light is emitted when an electron jumps from a higher state to a lower state He compared a quantized angular momentum to the Balmer series 27.12

27.12 Bohr Model Although the results worked n is an integer called the principle quantum number It was simply chosen because it worked The lowest E 1 – ground state Higher levels – excited state 27.12

27.12 Bohr Model The minimum energy level required to remove an electron from the ground state is called the ionization energy For hydrogen is it 13.6eV and precisely corresponds to the energy to go from E 1 to E=0 Often shown in an Energy Level Diagram Vertical arrows show transitions Energy released or absorvedcan be calculated by the difference between energy at each level 27.12

Early Quantum Theory de Broglie’s Hypothesis Applied to Atoms

Bohr could give no reason why electrons were quantized Reason was purposed by de Broglie A particle of mass moving with a nonrelativistic speed would have a wavelength such that If each electron orbit is treated as a standing wave we get This is the quantum condition purposed by Bohr 27.13