2 Problems which classical physics could not solve Blackbody RadiationE&M radiation emitted by a heated objectPhotoelectric EffectEmission of electrons by an illuminated metalX-Ray DiffractionThe Compton EffectSpectral Lines Emitted by Atoms
3 Blackbody RadiationAn object at any temperature is known to emit electromagnetic radiation, called thermal radiationStefan’s Law, the power radiated by an object, P = s A e T4T-temperature, A-area, e-emissivity, s= W/m2 K4The spectrum of the radiation depends on the temperature and properties of the object
4 Blackbody Radiation Graph The wavelength of the peak of the blackbody distribution was found to follow Wein’s Displacement Lawλmax T = x 10-2 m • Kλmax is the wavelength at the curve’s peak
5 The Ultraviolet Catastrophe and Planck’s theory Classical theory predicted infinite energy at low wavelengthsPlanck hypothesized that the blackbody radiation was produced by resonatorsThe resonators could only have discrete energiesEn = n h ƒn is called the quantum numberƒ is the frequency of vibrationh is Planck’s constant, x J s
6 Photoelectric Effect When light strikes E, photoelectrons are emitted Electrons collected at C and passing through the ammeter are a current in the circuitC is maintained at a positive potential by the power supply
7 Photoelectric Current/Voltage Graph Classical theory couldnot explain:The stopping potential is independent of the radiation intensityThe maximum kinetic energy of the photoelectrons is independent of the light intensityThe maximum kinetic energy of the photoelectrons increases with increasing light frequency
8 Einstein’s Explanation Light is a collection of photons (not waves)The photon’s energy would be E = hƒE=nhf-(n-1)hfEach photon can give all its energy to an electron in the metalThe maximum kinetic energy of the liberated photoelectron is KE = hƒ – ΦΦ is called the work function of the metal
9 Verification of Einstein’s Theory Problem What wavelength of light would have to fall on sodium (work function 2.46 eV) if it is to emit electrons with a maximum speed of 1.0 x 106 m/s?
10 Photocells Photocells are an application of the photoelectric effect When light of sufficiently high frequency falls on the cell, a current is producedExamplesStreetlights, garage door openers, elevators
11 Problem 27-13What wavelength of light would have to fall on sodium (with a work function of 2.46 eV) if it is to emit electrons with a maximum speed of 1.0 × 106 m/s?
12 X-Rays Electromagnetic radiation with short wavelengths Wavelengths less than for ultravioletWavelengths are typically about 0.1 nmX-rays have the ability to penetrate most materials with relative easeDiscovered and named by Roentgen in 1895
14 Schematic for X-ray Diffraction A continuous beam of X-rays is incident on the crystalThe diffracted radiation is very intense in certain directionsThese directions correspond to constructive interference from waves reflected from the layers of the crystal
16 Bragg’s LawBragg’s Law gives the conditions for constructive interference2 d sin θ = m λ m = 1, 2, 3…
17 Compton ScatteringCompton assumed the photons acted like other particles in collisionsEnergy and momentum were conservedThe shift in wavelength is
18 QUICK QUIZ 27.1An x-ray photon is scattered by an electron. The frequency of the scattered photon relative to that of the incident photon (a) increases, (b) decreases, (c) remains the same.
19 QUICK QUIZ 27.2A photon of energy E0 strikes a free electron, with the scattered photon of energy E moving in the direction opposite that of the incident photon. In this Compton effect interaction, the resulting kinetic energy of the electron is (a) E0 , (b) E , (c) E0 E , (d) E0 + E , (e) none of the above.
20 Photons and Electromagnetic Waves Light has a dual nature. It exhibits both wave and particle characteristicsApplies to all electromagnetic radiationThe photoelectric effect and Compton scattering offer evidence for the particle nature of lightInterference and diffraction offer evidence of the wave nature of light
21 Wave Properties of Particles In 1924, Louis de Broglie postulated that because photons have wave and particle characteristics, perhaps all forms of matter have both propertiesFurthermore, the frequency and wavelength of matter waves can be determined
22 de Broglie Wavelength and Frequency The de Broglie wavelength of a particle isThe frequency of matter waves is
23 QUICK QUIZ 27.3A non-relativistic electron and a non-relativistic proton are moving and have the same de Broglie wavelength. Which of the following are also the same for the two particles: (a) speed, (b) kinetic energy, (c) momentum, (d) frequency?
24 The Electron Microscope The electron microscope depends on the wave characteristics of electronsMicroscopes can only resolve details that are slightly smaller than the wavelength of the radiation used to illuminate the objectThe electrons can be accelerated to high energies and have small wavelengths
25 The Uncertainty Principle When measurements are made, the experimenter is always faced with experimental uncertainties in the measurementsClassical mechanics would allow for measurements with arbitrarily small uncertaintiesQuantum mechanics predicts that a barrier to measurements with ultimately small uncertainties does exist
26 Heisenberg’s Uncertainty Principle Mathematically,It is physically impossible to measure simultaneously the exact position and the exact linear momentum of a particleAnother form of the principle deals with energy and time:
27 Problem 27-43In the ground state of hydrogen, the uncertainty of the position of the electron is roughly 0.10 nm. If the speed of the electron is on the order of the uncertainty in its speed, how fast is the electron moving?
28 Thought Experiment – the Uncertainty Principle A thought experiment for viewing an electron with a powerful microscopeIn order to see the electron, at least one photon must bounce off itDuring this interaction, momentum is transferred from the photon to the electronTherefore, the light that allows you to accurately locate the electron changes the momentum of the electron
29 Scanning Tunneling Microscope (STM) Allows highly detailed images with resolution comparable to the size of a single atomA conducting probe with a sharp tip is brought near the surfaceThe electrons can “tunnel” across the barrier of empty space
30 Conceptual questions1. If you observe objects inside a very hot kiln, it is difficult to discern the shapes of the objects. Why?3. Are the blackbodies really black?9. In the photoelectric effect, explain why the stopping potential depends on the frequency of the light but not on the intensity.10. Which has more energy, a photon of ultraviolet radiation or a photon of yellow light?
31 Problems42. A 50-g ball moves at 30.0 m/s. If its speed is measured to an accuracy of 0.10%, what is the minimum uncertainty in its position?51. Photons of wavelength 450 nm are incident on a metal. The most energetic electrons ejected from the metal are bent into a circular arc of radius 20.0 cm by a magnetic field with a magnitude of 2.00 × 10–5 T. What is the work function of the metal?