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**Blackbody Radiation & Planck’s Hypothesis**

A blackbody is any object that absorbs all light incident upon it Shiny & reflective objects are poor blackbodies Recall: good absorbers and also good emitters Ideally we imagine a box with a small hole that very little light (EM radiation) can reflect back out

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**Note: As temp. increases – area under curve increases**

Consider heating blackbodies to various temperatures and recording intensity of radiation at differing frequencies At both low and high freq. there is very little radiation The rad. Peaks at an intermediate freq. This distribution holds true regardless of the material Note: As temp. increases – area under curve increases This represents total energy As temp. increases – peak moves to higher frequency

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**The temperature therefore indicates its emitted color and vice versa**

We can determine star temperature (surface) by analyzing its color Red stars are fairly cool, like the bolt shown But White, or Blue-White stars are very hot Our sun is intermediate

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**Planck’s Quantum Hypothesis**

Attempts to explain blackbody radiation using classical physics failed miserably At low temps. Prediction & exp match well At high temps. Classical prediction explodes to infinity Very different from experimental result Referred to as the Ultraviolet Catastrophe

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**German physicists Max Planck diligently tried to solve this issue**

He “stumbled” upon a mathematical formula that matched the experiment He then needed to derive the physical formula The only way was to assume energy (in the form of EM radiation) way quantized Little “packets” of energy

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E α f Inserting a constant, h E = n h f Where n = number of packets and h = planck’s constant h = 6.63 x J • s One of our fundamental constants of nature This tells us that energy can only change in quantum jumps, a very tiny amount not experienced everyday

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**It does explain the exp. quite well:**

Planck was not satisfied and believed (along with other physicists) that it was a purely mathematical solution, not a “real” physical one It does explain the exp. quite well: The > f, the > quantum of energy needed As frequency increased, the amount of energy needed for small jumps increased as well The object only has a certain amount of energy to supply Therefore: radiation drops to zero at high frequency

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**Photons & the Photoelectric Effect**

Planck believed that the atoms of a blackbody vibrated with discrete frequencies (like standing waves) But, at the time light was considered a wave therefore no connection Einstein took the idea of quanta of energy and applied it to light – called photons

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**Each photon has energy based on its frequency E = n h f **

A beam of light can be thought of as a beam of particles More intense = more particles Since each photon have small amounts of energy, there must be tremendous numbers of them

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**Einstein applied this model to the photoelectric effect issue**

Light hitting the surface of metals can cause electrons to be ejected The effect could not be explained using the wave theory of light We can determine the number of e ejected by connecting the apparatus to a simple circuit

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**Classical physics predicts **

light of any frequency should eject e as long as intensity is high enough The K of e should increase with intensity The minimum amount of energy needed to eject e = work function, W0 Metal dependent Usually a few eV If an e is given energy by light that exceeds W0, the additional amount goes into kinetic energy of e Kmax = E – W0

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**Both of these are explained using the photon model of light**

Changing intensity only changes the number of photons E is ejected only if the photon has sufficient energy (at least equal to the work function) The is the cutoff frequency, f0 These do not agree with experiment: There is a minimum frequency required – the cutoff frequency, f0 If f < f0 no e regardless of the intensity The Kmax of e depends only on the frequency Increasing intensity about f0 only increases the number of e

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**If f > f0, the e leaves metal with some K **

If f < f0, no e are ejected regardless of intensity Since energy is that of a photon Kmax = hf – W0 Therefore, Kmax depends linearly on frequency A plot of Kmax for Na & Au shows different cutoff frequencies, but the same slope, h

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**Photons & the Photoelectric Effect**

Quantization of light – Albert Einstein (1905) Based on properties of EM waves Emitted radiation should be quantized Quantum (packet of light) – photon Each photon has energy E = h f Little bundles of light energy Connection between wave & particle nature of light

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**Einstein used this to explain the photoelectric effect **

Certain metallic materials are photosensitive Light striking material emits electrons (e) The radiant energy supplies the work necessary to free the e – photoelectrons

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**Photocurrent until a saturation current is reached**

When photocell is illuminated with monochromatic light, characteristic curves are obtained Photocurrent until a saturation current is reached All emitted e reach anode voltage has no effect on current

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**Classically: > the intensity, the > energy of e**

K of e can be tested by reversing voltage Only e with enough K (eV) make it to the negative plate & contribute to the current As voltage , then is made negative, current At some voltage V0, the stopping potential, no current will flow

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**The max K (Kmax) is related to stopping potential**

eV = the work needed to stop e Kmax = eV0 When f of light is varied, the Kmax is found to depend linearly on f No photoemission is observed below cutoff frequency, f0

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**Emission begins the instant (~10-9 s) even with low intensity light**

Classically, time is required to “build up” energy Since light can be considered a “bundle of energy”, E = hf The e absorb whole photon or nothing Since e are bound by attractive forces, work must be done Conservation of energy hf = K + φ where φ = amount of work (energy) needed to free e Part of energy of photon “frees” e & the rest is carried away as K

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**Least tightly bound will have maximum K**

Does not change energy of individual photons Photon energy depends on frequency Below a certain freq. no e are dislodged When Kmax = 0 the minimum cutoff frequency, f0 Hf0 = Kmax + φ0 = 0 + φ0 f0 = φ0 / h Least tightly bound will have maximum K Energy needed = work function, φ0 hf = Kmax + φ0 Other e require more energy & the K is less Increasing light intensity, increases # of photons thus increasing # of e

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**Photon has enough energy to free e, but no extra to give it K**

Sometimes called threshold frequency Light below this (no matter how many) will not dislodge e

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Introduction to Quantum Physics

Introduction to Quantum Physics

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