General Physics (PHY 2140) Lecture 28 Modern Physics Quantum Physics Photoelectric effect http://www.physics.wayne.edu/~apetrov/PHY2140/ Chapter 27 9/19/2018

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Lightning Review Last lecture: Quantum physics Blackbody radiation Planck’s hypothesis Review Problem: All objects radiate energy. Why, then, are we not able to see all objects in a dark room? 9/19/2018

Reminder (for those who don’t read syllabus) Reading Quizzes (bonus 5%): It is important for you to come to class prepared, i.e. be familiar with the material to be presented. To test your preparedness, a simple five-minute quiz, testing your qualitative familiarity with the material to be discussed in class, will be given at the beginning of some of the classes. No make-up reading quizzes will be given. There could be one today… … but then again… 9/19/2018

QUICK QUIZ A photon (quantum of light) is reflected from a mirror. True or false: (a) Because a photon has a zero mass, it does not exert a force on the mirror. (b) Although the photon has energy, it cannot transfer any energy to the surface because it has zero mass. (c) The photon carries momentum, and when it reflects off the mirror, it undergoes a change in momentum and exerts a force on the mirror. (d) Although the photon carries momentum, its change in momentum is zero when it reflects from the mirror, so it cannot exert a force on the mirror. False True 9/19/2018

Problem: a lightbulb Assuming that the tungsten filament of a lightbulb is a blackbody, determine its peak wavelength if its temperature is 2 900 K. 9/19/2018

This is infrared, so most of the electric energy goes into heat! Assuming that the tungsten filament of a lightbulb is a blackbody, determine its peak wavelength if its temperature is 2 900 K. Recall Wein;s law: λmax T = 0.2898 x 10-2 m • K. It can be used to solve for lmax: Given: T = 2900 K Find: lmax = ? Thus, This is infrared, so most of the electric energy goes into heat! 9/19/2018

27.2 Photoelectric Effect When light is incident on certain metallic surfaces, electrons are emitted from the surface This is called the photoelectric effect The emitted electrons are called photoelectrons The effect was first discovered by Hertz The successful explanation of the effect was given by Einstein in 1905 Received Nobel Prize in 1921 for paper on electromagnetic radiation, of which the photoelectric effect was a part 9/19/2018

Photoelectric Effect Schematic When light strikes E, photoelectrons are emitted Electrons collected at C and passing through the ammeter are a current in the circuit C is maintained at a positive potential by the power supply 9/19/2018

Photoelectric Current/Voltage Graph The current increases with intensity, but reaches a saturation level for large ΔV’s No current flows for voltages less than or equal to –ΔVs, the stopping potential The stopping potential is independent of the radiation intensity 9/19/2018

Features Not Explained by Classical Physics/Wave Theory No electrons are emitted if the incident light frequency is below some cutoff frequency that is characteristic of the material being illuminated The maximum kinetic energy of the photoelectrons is independent of the light intensity The maximum kinetic energy of the photoelectrons increases with increasing light frequency Electrons are emitted from the surface almost instantaneously, even at low intensities 9/19/2018

Einstein’s Explanation A tiny packet of light energy, called a photon, would be emitted when a quantized oscillator jumped from one energy level to the next lower one Extended Planck’s idea of quantization to electromagnetic radiation The photon’s energy would be E = hƒ Each photon can give all its energy to an electron in the metal The maximum kinetic energy of the liberated photoelectron is KE = hƒ – Φ Φ is called the work function of the metal 9/19/2018

Explanation of Classical “Problems” The effect is not observed below a certain cutoff frequency since the photon energy must be greater than or equal to the work function Without this, electrons are not emitted, regardless of the intensity of the light The maximum KE depends only on the frequency and the work function, not on the intensity The maximum KE increases with increasing frequency The effect is instantaneous since there is a one-to-one interaction between the photon and the electron 9/19/2018

Verification of Einstein’s Theory Experimental observations of a linear relationship between KE and frequency confirm Einstein’s theory The x-intercept is the cutoff frequency 9/19/2018

Problem: photoeffect Electrons are ejected from a metallic surface with speeds ranging up to 4.6 × 105 m/s when light with a wavelength of λ = 625 nm is used. (a) What is the work function of the surface? (b) What is the cutoff frequency for this surface? 9/19/2018

(a) What is the work function of the surface? Electrons are ejected from a metallic surface with speeds ranging up to 4.6 × 105 m/s when light with a wavelength of λ = 625 nm is used. (a) What is the work function of the surface? (b) What is the cutoff frequency for this surface? Recall that KEmax=hf - f. This can be used to solve for f. First find the kinetic energy Given: v = 4.6x105 m/s l = 625 nm Find: f = ? n =? Thus, It equals to 1.4 eV Cutoff frequency is 9/19/2018

27.3 Application: Photocells Photocells are an application of the photoelectric effect When light of sufficiently high frequency falls on the cell, a current is produced Examples Streetlights, garage door openers, elevators 9/19/2018

27.4 X-Rays Electromagnetic radiation with short wavelengths Wavelengths less than for ultraviolet Wavelengths are typically about 0.1 nm X-rays have the ability to penetrate most materials with relative ease Discovered and named by Roentgen in 1895 9/19/2018

Production of X-rays X-rays are produced when high-speed electrons are suddenly slowed down Can be caused by the electron striking a metal target A current in the filament causes electrons to be emitted These freed electrons are accelerated toward a dense metal target The target is held at a higher potential than the filament 9/19/2018

Production of X-rays An electron passes near a target nucleus The electron is deflected from its path by its attraction to the nucleus This produces an acceleration It will emit electromagnetic radiation when it is accelerated 9/19/2018

Diffraction of X-rays by Crystals For diffraction to occur, the spacing between the lines must be approximately equal to the wavelength of the radiation to be measured For X-rays, the regular array of atoms in a crystal can act as a three-dimensional grating for diffracting X-rays 9/19/2018

Schematic for X-ray Diffraction A continuous beam of X-rays is incident on the crystal The diffracted radiation is very intense in certain directions These directions correspond to constructive interference from waves reflected from the layers of the crystal The diffraction pattern is detected by photographic film 9/19/2018

Photo of X-ray Diffraction Pattern The array of spots is called a Laue pattern The crystal structure is determined by analyzing the positions and intensities of the various spots This is for NaCl 9/19/2018

Bragg’s Law The beam reflected from the lower surface travels farther than the one reflected from the upper surface If the path difference equals some integral multiple of the wavelength, constructive interference occurs Bragg’s Law gives the conditions for constructive interference 2 d sin θ = m λ, m = 1, 2, 3… 9/19/2018

If you want to know your progress so far, please send me an email request at apetrov@physics.wayne.edu 9/19/2018