UH PHYS 1302 - Ch30 (13 pages)

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Ch30



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Ch30

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ch 30 study guide


Pages:
13
School:
University of Houston
Course:
Phys 1302 - Introductory to Physics II
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Chapter 30 Quantum Physics 1 Blackbody Radiation and Planck s Hypothesis of Quantized Energy A blackbody is an idealized object that absorbs all incident radiation A blackbody at a fixed temperature T is a perfect emitter of radation The distribution of the amount of radiation given off by a blackbody of temperature T versus the frequency of the radiation f is shown in the figure This distribution is the same for any blackbody regardless of the material from which the blackbody is made It only depends on the temperature 1 As the temperature increases the total amount of energy radiated area under the curve increases Hotter objects radiate more energy L Whitehead 1 Phys 1302 2 As the temperature increases the peak frequency the frequency at which the blackbody emits the most energy increases The relationship between the peak frequency and temperature is given by Wien s displacement law fpeak 5 88 1010 sK 1 T 1 Kelvin K is a unit of temperature TK TC 273 15 where TK is the temperature in Kelvin and TC is the temperature in Celsius This relationship means that the color of a hot object is related to its temperature A hot stovetop appears red An object that glows red is at a lower temperature than an object that glows blue because fred fblue The sun has a surface temperature of 5800 K What is the peak frequency of radiation emitted by the Sun fpeak 5 88 1010 sK 1 T 5 88 1010 sK 1 5800K 3 4 1014 Hz This is in the infrared portion of the EM spectrum Blackbody radiation was understood experimentally in the late 1800 s but a theoretical explanantion for the results couldn t be found based on classical physics German physicist Max Planck was finally able to derive an expression for the frequency spectrum by making this assumption The radiation energy of a blackbody at frequency f must be an integral multiple of a constant h times the frequency En nhf n 0 1 2 3 2 We say that the energy is quantized It is not a continuous spectrum the energy can only take on certain values Planck s constant h 6 63 10 34 Js Classically energy can be any value from zero to infinity For classical waves like sound waves the energy of the wave depends only on the amplitude not the freqency This was the beginning of quantum physics Because of the quantization L Whitehead 2 Phys 1302 energy can only change in small discrete amounts equal to hf 2 Photons and the Photoelectric Effect Some physicists didn t really buy that a blackbody really had quantized energy because they thought of light as a wave remember Young s double slit experiment and a wave can have any energy Einstein took the idea seriously though and proposed that light comes in bundles of energy called photons Light with frequency f consists of many photons which each have an energy E hf 3 In this model a beam of light can be though of as a beam of particles each carrying energy hf Higher intensity means that more photons pass a given point in a given amount of time i e the photons are more tightly packed together But each individual photon in the beam has the same energy What is the energy of a photon of red light with frequency 4 60 1014 Hz E hf 6 63 10 34 Js 4 60 1014 Hz 3 05 10 19 J A single photon has a very small amount of energy compared to macroscopic objects Suppose a light bulb converts 5 00 W of its power to red light frequency 4 60 1014 Hz How many photons are emitted in one second by the lightbulb E t N hf P t P t N hf 5 00J s 1s 3 05 10 19 J 1 64 1019 photons P L Whitehead 3 Phys 1302 What is the intensity of the light 1 m away from the bulb P A 5 00W 4 1m 2 0 398W m2 0 398J sm2 I How many photons are absorbed in one second by your eye area 2 0 10 5 m2 if you are standing 1 m away Remember intensity is the energy absorbed by a given area in a given time Peye IAeye E IAeye t N hf IAeye t IAeye t N hf 0 398J sm2 2 0 10 5 m2 1s 3 05 10 19 J 2 61 1013 photons If you get further away the intensity will decrease and so will the number of photons hitting your eye per second The photoelectric effect is a process in which light hitting the surface of a metal causes an electron to be emitted from the metal The ejected electron is referred to as a photoelectron L Whitehead 4 Phys 1302 With an apparatus as shown in the figure light shines on a metal plate and photoelectrons are ejected The photoelectrons are attracted to a positively charged collector plate which creates an electric current in the circuit that can be measured with the ammeter The minimum amount of energy necessary to eject an electron from a particular metal is called the work function W0 The work function is different for different materials The metal must be given energy E from the light beam greater than W0 to eject an electron E W0 If the energy is less than that no electron will be emitted The maximum kinetic energy a photoelectron can have is Kmax E W0 4 According to classical physics basically if you assume that light behaves like any other wave 1 A beam of light of any frequency any color can eject electrons as long as the intensity is great enough 2 The maximum kinetic energy of a photoelectron should increase as the intensity of the light increases But when the experiment was performed both of the above predictions were shown to be incorrect The observed behavior 1 The light must have a frequency greater than some minimum value to eject electrons If the frequency of the light is below this cutoff frequency f0 it will not eject electrons no matter what the intensity is 2 The maximum kinetic energy of the photoelectrons does not depend on the intensity it depends only the frequency In the photon model one photon gets absorbed by the metal If that absorbed energy the energy of the photon hf is greater than the work function hf W0 an electron will be ejected Thus the frequency of the photon must be at least f0 W0 h 5 for an electron to be ejected This is the definition of the cutoff frequency f0 If the intensity of the light is increased this means the number of photons hitting the surface in a given time is increased Since each photon can eject one electron L Whitehead 5 Phys 1302 more photons in a given time means more photoelectrons in a given time The maximum kinetic energy of the electron depends on how much of the photon energy is left over in excess of what is absorbed by the metal W0 …


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