1. 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

2. 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

3. 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

4. Incandescent Spectra produced from Thermal Radiation
intensity
Animation
frequency 4

5. 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

6. 6

7. 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

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

9. 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

10. 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

11. 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 n
the number of photo electrons
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

12. 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 nh n
In order for electrons to be emitted they must pass through
surface . \
use f
amount of energy to overcome surface
barrier
Ionization Potential
Work Function K = h n - f = h n - h n
max c 12

13. Einsteins Theory Predicts1 . K = h n - f ;
so K
depends on n
max
max 2 . h n 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

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

15. [ ] ( ) ( ) 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

16. What is Light?

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

18. Atomic Spectra 17

19. Absorption Spectra
gas
gas
Emission Spectra 18

20. 19

21. 20

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

23. Bohr Model

24. 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

25. - ( ) ( ) ( ) kq q e U r = = - k r r k = coulombs constant 1 e E r = K2 ( ) 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

26. Quantization of Angular Momentumß 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

27. 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