4: Introduction to Quantum Physics Blackbody Radiation and Planck’s Hypothesis The Photoelectric Effect Compton Effect Atomic Spectra The Bohr Quantum Model of the Atom 1

Material objects obey Newtons Laws of Motion Classical Physics Material objects obey Newtons Laws of Motion Electricity and Magnetism obey Maxwells Equations Position and momentum are defined at all times Initial Position and momentum plus knowledge of all forces acting on system predict with certainty the position and momentum at all later times. Could not explain Black Body Radiation Photo Electric Effect Discrete Spectral Lines 2

Blackbody Radiation and Planck’s Hypothesis Classical explanation Any object with a temperature T>0 K radiates away thermal energy through the emission of electromagnetic radiation Classical explanation heat causes accelerated charges (Maxwell like distribution of accelerations) that emit radiation of various frequencies 3

Incandescent Spectra produced from Thermal Radiation intensity Animation frequency 4

Wiens Displacement Law = 2 . 898 mK max Rayleigh - Jeans Law 2 p ckT I ( l , T ) = l 4 Intensity of radiation of wavelength l at temp T However this only agrees with experiment at long l Lim I ( l , T ) = ¥ Ultraviolet Catastrophe l ¯ ( Þ ¥ total energy density ) 5

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En = energy of quantum state n of molecule Planck’s Assumptions Oscillating molecules that emit the radiation only have discrete energies En = nhn n = quantum number En = energy of quantum state n of molecule Molecules emit or absorb energy in discrete units of light called QUANTA 7

E2 hn hn=E E1 E = E2-E1 8

Animation The Photoelectric Effect Light A Electron G V A is maintained at a positive potential by battery. IG = 0 until monochromatic light of certain l is incident G V Animation 9

plate A has negative potential high intensity light low intensity light -V0 V plate A has negative potential Stopping Potential When A is negative only electrons having K.E. > eV0 will reach A, independent of light intensity Maximum K.E. of ejected electrons Kmax= eV0 10

Wave theory of light does not predict such properties Observed Properties 1 . No electrons ejected if n £ n (cut off frequency ) c 2 . If n ³ n the number of photo electrons µ light intensity c 3 . K is independent of light intensity max 4. K ­ as n ­ max 5 . Electrons are emitted instantaneously even at low light intensities Wave theory of light does not predict such properties 11

Einstein explained this by the hypothesis that light is quantized in energy packets = QUANTA with energy E = h n he called such quanta PHOTONS . The intensity of the light is proportional to the number of such quanta i . e . I µ nh n In order for electrons to be emitted they must pass through surface . \ use f amount of energy to overcome surface barrier º Ionization Potential º Work Function K = h n - f = h n - h n max c 12

Einsteins Theory Predicts 1 . K = h n - f ; so K depends on n max max 2 . h n ³ f ; for emission of electrons 3 . h n - f only depends on n not on intensity 4. K ­ as n ­ max 5 . single electrons are excited by light (not many gradually) Þ instantaneous emission Kmax = hn-f slope = h Kmax nc 13

More Evidence that light is composed of particles Compton Effect q f scattered photon scattered electron 14

[ ] ( ) ( ) Observed scattering intensity I I = I l , q ; incident l ¹ scattered l - this contradicts classical theory D l = l - l Compton ( 1923 ) suggested treating photon as particle hc E = h n = l The Special Theory of Relativity gives E = pc [ p is the magnitude of the momentum of the photon ] hc h \ pc = Þ p = l l D E = D p = tot tot h Þ D l = ( 1 - cos q ) m c e Þ l ­ ; n ¯ ; E ¯ during collision photon h Compton Wavelength of electron = m c e 15

What is Light?

Youngs Double Slit Experiment Light is composed of waves Photo Electric Effect Light is composed of particles Compton Effect Paradox? Wave Particle Duality 16

Atomic Spectra 17

Absorption Spectra gas gas Emission Spectra 18

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æ 1 1 1 ö ç = R - ÷ ; n = n + 1 , n + 2 , K l è n n ø R = 1 . 0973732 H è n 2 n 2 ø 2 1 1 1 2 7 R = 1 . 0973732 ´ 10 m-1 º Rydberg Constant H n = 1 Û Lyman 1 n = 2 Û Balmer 1 n = 3 Û Paschen 1 n = 4 Û Brackett 1 21

Bohr Model

Animation Angular Momentum Quantization 1 . Electron moves in circular orbit about nucleus 2 . Electron can only exist in specific orbits determined by Angular Momentum Quantization h L = m v r = I w = n = n h ; n = 1 , 2 , K e 2 p é v ù I = mr ; w = 2 ë r û 3 . Electrons in such orbits DO NOT radiate energy although they are accelerating. Such orbits are thus called STATIONARY STATES 4. Atoms radiate only when electron jumps from higher energy (large radius ) to lower energy (smaller radius ) orbits . The frequency of light they radiate is given by E - E Animation n = h l h 22

- ( ) ( ) ( ) kq q e U r = = - k r r k = coulombs constant 1 e E r = K 2 ( ) U r = 1 2 = - k r r k = coulombs constant - 1 e 2 ( ) r E r = K + U = m v - k 2 2 e r + If electrons speed is constant m v 2 e 2 e 2 F = m a = e = k Þ m v 2 = k c e c r r 2 e r 1 1 e 2 \ m v 2 = k 2 e 2 r 1 e 2 Þ E ( r ) = - k 2 r 23

Quantization of Angular Momentum ß n h n h r = Û v = m v m r e e n 2 h ke 2 2 \ m v 2 = = e m r 2 r e n 2 h 2 Þ r = ; n = 1 , 2 , K m ke 2 e \ r = r i . e . r depends on n n h 2 Bohr radius is defined as r = m ke 2 e so that r = n r 2 n 24

for the energy we obtain using these values for r in the expression n for the energy we obtain m k 2 e 4 æ 1 ö E = - e ; n = 1 , 2 , K 2 è n ø n h 2 2 æ 1 ö = - 13 . 6 eV è ø n 2 thus the frequencies of emitted photons are E - E m k æ 2 e 4 1 1 ö n = 2 1 = e ç - ÷ 21 h 2h h n n 2 è 2 2 ø 1 2 1 n m k æ 2 e 4 1 1 ö = = ç e - ÷ l c 2h h 2 c è n 2 n 2 ø 1 2 Theoretical expression for Rydberg constant m k 2 e 4 R = e H 2h h 2 c which is in good agreement with experimental value 25