PHYS-3301 Lecture 3. EM- Waves behaving like Particles. CHAPTER 3 The Experimental Basis of Quantum. CHAPTER 3 The Experimental Basis of Quantum

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CHAPTER 3 The Experimetal Basis of Quatum PHYS-3301 Lecture 3 Sep. 4, 2018 3.1 Discovery of the X Ray ad the Electro 3.2 Determiatio of Electro Charge 3.

9 Pair Productio ad Aihilatio EM- Waves behavig like Particles CHAPTER 3 The Experimetal Basis of Quatum 3.1 Discovery of the X Ray ad the Electro 3.

6 Photoelectric Effect (Eistei; 1905; 1921*) 3.7 X-Ray Productio (Rötge;1895; 1901*) 3.8 Compto Effect (Compto; 1927; 1927*) 3.

1 CHAPTER 3 The Experimetal Basis of Quatum PHYS-3301 Lecture 3 Sep. 4, Discovery of the X Ray ad the Electro 3.2 Determiatio of Electro Charge 3.3 Lie Spectra 3.4 Quatizatio 3.5 Blackbody Radiatio 3.6 Photoelectric Effect 3.7 X-Ray Productio 3.8 Compto Effect 3.9 Pair Productio ad Aihilatio EM- Waves behavig like Particles CHAPTER 3 The Experimetal Basis of Quatum 3.1 Discovery of the X Ray ad the Electro 3.2 Determiatio of Electro Charge 3.3 Lie Spectra Today 3.4 Quatizatio 3.5 Blackbody Radiatio (Plak; 1900; 1918*) 3.6 Photoelectric Effect (Eistei; 1905; 1921*) 3.7 X-Ray Productio (Rötge;1895; 1901*) 3.8 Compto Effect (Compto; 1927; 1927*) 3.9 Pair Productio ad Aihilatio (Aderso; 1932; 1936*) 3.1: Discovery of the X Ray ad the Electro X rays were discovered by Wilhelm Rötge i q Observed x rays emitted by cathode rays bombardig glass Electros were discovered by J. J. Thomso. q Observed that cathode rays were charged particles

2 Cathode Ray Experimets I the 1890s scietists ad egieers were familiar with cathode rays. These rays were geerated from oe of the metal plates i a evacuated tube across which a large electric potetial had bee established. Cathode Ray Experimets It was guessed that cathode rays had somethig to do with atoms. It was kow that cathode rays could peetrate matter ad their properties were uder itese ivestigatio durig the 1890s. Observatio of X Rays Rötge s X Ray Tube Wilhelm Rötge studied the effects of cathode rays passig through various materials. He oticed that a phosphorescet scree ear the tube glowed durig some of these experimets. These rays were uaffected by magetic fields ad peetrated materials more tha cathode rays. He called them x rays ad deduced that they were produced by the cathode rays bombardig the glass walls of his vacuum tube. Rötge costructed a x-ray tube by allowig cathode rays to impact the glass wall of the tube ad produced x rays. He used x rays to image the boes of a had o a phosphorescet scree.

Rötge s X Ray Tube Rötge costructed a x-ray tube by allowig

the electro s charge to mass (q/m) was to sed electros

evacuated cathode-ray tube to show that the cathode rays were

3 Rötge s X Ray Tube Rötge costructed a x-ray tube by allowig cathode rays to impact the glass wall of the tube ad produced x rays. He used x rays to image the boes of a had o a phosphorescet scree. Thomso s Experimet Thomso s method of measurig the ratio of the electro s charge to mass (q/m) was to sed electros through a regio cotaiig a magetic field perpedicular to a electric field. Apparatus of Thomso s Cathode-Ray Experimet Thomso used a evacuated cathode-ray tube to show that the cathode rays were egatively charged particles (electros) by deflectig them i electric ad magetic fields. Calculatio of e/m A electro movig through the electric field is accelerated by a force: Electro agle of deflectio: The magetic field deflects the electro agaist the electric field force. The magetic field is adjusted util the et force is zero. Charge to mass ratio:

3.2: Determiatio of Electro Charge Millika oil drop experimet Calculatio of the oil drop charge Used a electric field ad gravity to susped a charged oil drop (also, E = V/d) Diagram of the Millika

4 3.2: Determiatio of Electro Charge Millika oil drop experimet Calculatio of the oil drop charge Used a electric field ad gravity to susped a charged oil drop (also, E = V/d) Diagram of the Millika oil-drop experimet to measure the charge of the electro. Some of the oil drops from the atomizer emerge charged, ad the electric field (voltage) is varied to slow dow or reverse the directio of the oil drops, which ca have positive or egative charges. Magitude of the charge o the oil drop Mass is determied from Stokes s relatioship of the termial velocity to the radius ad desity Thousads of experimets showed that there is a basic quatized electro charge C 3.3: Lie Spectra Optical Spectrometer Chemical elemets were observed to produce uique wavelegths of light (colors) whe bured or excited i a electrical discharge. Collimated light is passed through a diffractio gratig with thousads of rulig lies per cetimeter. q The diffracted light is separated at a agle q accordig to its wavelegth λ by the equatio: where d is the distace betwee ruligs ad is a iteger called the order umber Diffractio creates a lie spectrum patter of light bads ad dark areas o the scree. Wavelegths of these lie spectra allow idetificatio of the chemical elemets ad the compositio of materials.

Balmer Series Rydberg Equatio I 1885, Joha Balmer foud a empirical formula for wavelegth of the visible hydroge lie spectra i m: As more scietists discovered emissio lies at ifrared ad ultraviolet

5 Balmer Series Rydberg Equatio I 1885, Joha Balmer foud a empirical formula for wavelegth of the visible hydroge lie spectra i m: As more scietists discovered emissio lies at ifrared ad ultraviolet wavelegths, the Balmer series equatio was exteded to the Rydberg equatio: m (where k = 3,4,5 ad k > 2) ( = 2) The Balmer series of lie spectra of the hydroge atom with wavelegths idicated i aometers. The four visible lies are oted as well as the lower limit of the series. 3.4: Quatizatio Curret theories predict that charges are quatized i uits (quarks) of e/3 ad 2e/3, but quarks are ot directly observed experimetally. The charges of particles that have bee directly observed are quatized i uits of e. The measured atomic weights are ot cotiuous they have oly discrete values, which are close to itegral multiples of a uit mass. 3.5: Blackbody Radiatio Whe matter is heated, it emits radiatio. A blackbody is a cavity i a material that oly emits thermal radiatio. Icomig radiatio is absorbed i the cavity. A approximate realizatio of a black body as a tiy hole i a isulated eclosure I physics, a blackbody is a idealized object that absorbs all icidet E&M radiatio. No E&M radiatio passes through the blackbody ad oe is reflected. Because o light is reflected or trasmitted, the object appears black whe it is cold.

3.5: Blackbody Radiatio Whe matter is heated, it emits radiatio. However, A blackbody a blackbody is a cavity emits i a temperature-depedet spectrum material of that light. oly (see emits the Fig.

6 3.5: Blackbody Radiatio Whe matter is heated, it emits radiatio. However, A blackbody a blackbody is a cavity emits i a temperature-depedet spectrum material of that light. oly (see emits the Fig.) thermal radiatio. Icomig radiatio is absorbed i the This cavity. thermal radiatio from a blackbody is termed black-body radiatio. I As physics, the temperature a blackbody decreases, is a the peak idealized object that absorbs of the black-body all icidet radiatio E&M curve radiatio. moves No E&M radiatio to lower itesities ad loger passes through the blackbody ad oe is reflected. wavelegths. A approximate realizatio of a black body as a tiy hole i a isulated eclosure Wie s Displacemet Law The itesity (λ, T) is the total power radiated per uit area per uit wavelegth at a give temperature. Wie s displacemet law: The maximum of the distributio shifts to smaller wavelegths as the temperature is icreased. (where l max = wavelegth of the peak) Because o light is reflected or trasmitted, the object appears black whe it is cold. Stefa-Boltzma Law The total power radiated icreases with the temperature: Rayleigh-Jeas Formula Lord Rayleigh used the classical theories of electromagetism ad thermodyamics to show that the blackbody spectral distributio should be This is kow as the Stefa-Boltzma law, with the costat σ experimetally measured to be W / (m 2 K 4 ). The emissivity є (є = 1 for a idealized blackbody) is simply the ratio of the emissive power of a object to that of a ideal blackbody ad is always less tha 1. It approaches the data at loger wavelegths, but it deviates badly at short wavelegths. This problem for small wavelegths became kow as the ultraviolet catastrophe ad was oe of the outstadig exceptios that classical physics could ot explai.

Black Body Radiatio (Max Plack 1900) Experimet shows that as frequecy icreases, the blackbody spectral eergy desity reaches a max. the fall off. But, classical theory predicts a divergece!

7 Black Body Radiatio (Max Plack 1900) Experimet shows that as frequecy icreases, the blackbody spectral eergy desity reaches a max. the fall off. But, classical theory predicts a divergece!! Do we eed a ew theory? Plack s Radiatio Law I 1900, Plack suggested a solutio based a revolutioary ew idea: Emissio ad absorptio of E&M radiatio by matter has quatum ature: i.e. the eergy of a quatum of E&M radiatio emitted or absorbed by a harmoic oscillator with the frequecy f is give by the famous Plack s formula (More i Appedix C) E = h f -34,where h is the Plack s costat h» J s - at odds with the classical traditio, where eergy was always associated with amplitude, ot frequecy Also, i terms of the w = 2p f E =! w where! = agular frequecy 2 h p!» J s The Plack s Black-Body Radiatio Law: The Eergy (E) i the electromagetic radiatio at a give frequecy (f) may take o values restricted to E = hf where: = a iteger h = a costat h ( Plack Costat ) -34» J s Blackbody Radiatio: A New Fudametal Costat Plak s spectral eergy desity is the critical lik betwee temperature ad E&M radiatio. Iterestigly, although the assumptio E = hf might suggest EM radiatio behavig as a itegral umber of particles of eergy hf, he hesitated at the ew frotier - others carried the revolutio forward. For the discovery, Plak was awarded the Nobel prize i 1918!!

8 Experimetal Fact: E = hf BUT Why should the eergy of a Electromagetic wave be Quatized? (= iteger) No Explaatio util 1905 Albert Eistei The Photoelectric Effect A wave is a Cotiuous Pheomeo Plack s Radiatio Law Plack assumed that the radiatio i the cavity was emitted (ad absorbed) by some sort of oscillators that were cotaied i the walls. He used Boltzma s statistical methods to arrive at the followig formula that fit the blackbody radiatio data. Plack s radiatio law Plack made two modificatios to the classical theory: 1) The oscillators (of electromagetic origi) ca oly have certai discrete eergies determied by E = hf, where is a iteger, f is the frequecy, ad h is called Plack s costat. h = J s. 2) The oscillators ca absorb or emit eergy i discrete multiples of the fudametal quatum of eergy give by

Experimental Fact: E = nhf

Experimental Fact: E = nhf CHAPTR 3 The xperimetal Basis of Quatum PHYS-3301 Lecture 4 Sep. 6, 2018 3.1 Discovery of the X Ray ad the lectro 3.2 Determiatio of lectro Charge 3.3 Lie Spectra 3.4 Quatizatio 3.5 Blackbody Radiatio