Presentation on theme: "Early Quantum Theory and Models of the Atom"— Presentation transcript:
1Early Quantum Theory and Models of the Atom Chapter 27Early Quantum Theory and Models of the Atom
227.1 Discovery and Properties of the Electron In the late 19th century, discharge tubes were made that emitted “cathode rays.”
327.1 Discovery and Properties of the Electron It was found that these rays could be deflected by electric or magnetic fields.
4Centripetal & Electric forces What happens to the charge particle as it enters the B field?x x x x x x x x x x x xvIf an electric field is turn on, the particles direction can be straighten out.Sometimes it is convenient to express the path of a particle in terms of its charge to mass ratioe is the charge on an electron
5Properties of the Electron By accelerating the rays through a known potential and then measuring the radius of their path in a known magnetic field, the charge to mass ratio could be measured:The result is
7Millikan’s Oil-drop experiment The force due to gravity (mg) was balanced by electric force created by an electric field.The mass and charge of each droplet were measuredAnalysis showed that the charge was always an integral multiple of a smallest charge, e.
8Quantized energy levels Ramp versus stair analogy. On a ramp, a box can have continuous values of potential energy.On the stairs, the box can have only discrete (quantized) values of energy
9Photon Theory of Light and the Photoelectric Effect Einstein suggested that, given the success of Planck’s theory, light must be emitted in small energy packets:These tiny packets, or particles, are called photons.
10Quantum numberPlanck proposed that energy of any molecular vibration can only be a whole number of hfn is the quantum number or number of photonsh is Planck’s constant
11Photoelectric Effect The photoelectric effect: When light strikes a metal, electrons are emitted.
12Photon Theory of Light and the Photoelectric Effect Recall chapters 23 & 24 explained reflection, diffraction, and interference using ray diagrams and the theory that light behaves as a waveIf light is a wave, theory predicts:Number of electrons and their energy should increase with intensityFrequency would not matter
13Photon Theory of Light and the Photoelectric Effect If light is particles, theory predicts:Increasing intensity increases number of electrons but not energyAbove a minimum energy required to break atomic bond, kinetic energy will increase linearly with frequencyThere is a cutoff frequency below which no electrons will be emitted, regardless of intensity
14Photon Theory of Light and the Photoelectric Effect A photon with a frequency of red light strikes an electron, but only excites it to a higher energy state.A photon with a frequency of green light strikes an electron with enough energy to release it from the metal, but it has no KE after being releasedA photon with a frequency of blue light strikes an electron and releases with some velocity.
15Photon Theory of Light and the Photoelectric Effect hf : is the energy of the incoming photonɸ :is the work function, the energy required to break the electron freeKE : is the kinetic energy of the released electron
16Increasing the intensity of light (100W bulb vs. 60W bulb)Increasing the intensity of light does not increase the energy of the photon.It does increase the number of photons, which increases the number of ejected electrons (more current).
17Photon Theory of Light and the Photoelectric Effect The particle theory assumes that an electron absorbs a single photon.Plotting the kinetic energy vs. frequency:
18If the photon doesn’t have sufficient energy to release the electron, it can be “excited” to a higher energy state.The electrons in free atoms can only be found in only certain discrete energy states.When the electrons fall back to the “ground state”, they release a very specific spectrum of light
2027.12 The Bohr AtomThe lowest energy level is called the ground state; the others are excited states.Z is the # of Chargesn is the Energy State
21Energy, Mass, and Momentum of a Photon When objects travel close to or at the speed of light, relativistic equations for length, time and momentum must be observedPhotons travel at the speed of light.If v = c, then the denominator is zero which can only happen if the rest mass of the photon is zero.This means a photon can never be at rest
22Compton EffectThis is another effect that is correctly predicted by the photon model and not by the wave model.
23Compton EffectCompton found that the scattered X-rays had a slightly longer wavelength than the incident ones, and that the wavelength depended on the scattering angle:This means the exiting photon has less energy
24Photon Interactions; Pair Production In pair production, energy, electric charge, and momentum must all be conserved.The photon disappears and creates an electron-positron pair.Rest mass is being created from pure energy:E=mc2
25In pair production, energy, electric charge, and momentum must all be conserved. Energy is conserved through the mass and kinetic energy of the electron and positronCharge is conserve by creating both a positive and negative charge.The interaction must take place in the electromagnetic field of a nucleus, which conserves momentum.
26Photon Interactions; Pair Production Photons passing through matter can undergo the following interactions:Photoelectric effect: photon is completely absorbed, electron is ejectedPhoton may be totally absorbed by electron, but not have enough energy to eject it; the electron moves into an excited stateThe photon can scatter from an atom and lose some energyThe photon can produce an electron-positron pair.
27Wave-Particle Duality; The Principle of Complementarity Phenomena such as diffraction and interference show that light is a wavePhenomena such as the photoelectric effect and the Compton effect that show that it is a particle.Which is it?This question has no answer; we must accept the dual wave-particle nature of light.
28Wave Nature of MatterJust as light sometimes behaves as a particle, matter sometimes behaves like a wave.The wavelength of a particle of matter is:
29Early Models of the Atom Rutherford’s model of the atom is mostly empty space:
3027.11 Atomic Spectra: Key to the Structure of the Atom An atomic spectrum is a line spectrum – only certain frequencies appear. If white light passes through such a gas, it absorbs at those same frequencies.
31Key to the Structure of the Atom Atomic Spectra:Key to the Structure of the AtomA portion of the complete spectrum of hydrogen is shown here. The lines cannot be explained by the Rutherford theory.
32The Bohr AtomBohr proposed that the possible energy states for atomic electrons were quantized – only certain values were possible. Then the spectrum could be explained as transitions from one level to another.
33Summary of Chapter 27Planck’s hypothesis: molecular oscillation energies are quantizedLight can be considered to consist of photons, each of energyPhotoelectric effect: incident photons knock electrons out of material
34Summary of Chapter 27Compton effect and pair production also support photon theoryWave-particle duality – both light and matter have both wave and particle propertiesWavelength of an object: