1. CHAPTER 3 The Experimental Basis of Quantum Physics
3.1 Discovery of the X Ray and the Electron
3.2 Determination of Electron Charge
3.3 Line Spectra
3.4 Quantization
3.5 Blackbody Radiation
3.6 Photoelectric Effect
3.7 X-Ray Production
3.8 Compton Effect
3.9 Pair Production and Annihilation
All related to quantization  Quantum mechanics

2. Quantum? Quantum mechanics?
Quantum is the Latin word for amount and, in modern understanding, means the smallest possible discrete unit of any physical property, such as energy or matter.
(WhatIs.com)
(quantus = how much, quantum = noun form of quantus)
Quantum : 1.양자 2.몫 3.분량 (Daum 영어사전)
What are quantized?
 Energy (discrete energy levels), mass & charge quantization

3. Quantum mechanics Classical theory Why are things quantized?
Relativity
Why are things quantized?
 ???
Size
Quantum
mechanics
Why is QM important here?
 Quantization is more visible in microscopic world
Practically, quantum effect easily observable for…
 Electrons (thus atoms) and light.
Speed

4. Contents … Chapter 3 : The Experimental Basis of Quantum Physics
Chapter 4 : Structure of the Atom
Chapter 5 : Wave Properties of Matter and Quantum Mechanics I
Chapter 6 : Quantum Mechanics II
Chapter 7 : The Hydrogen Atom
Chapter 8 : Atomic Physics

5. X Ray
“Cathode rays” well known to scientists (first observed by Johann Hittorf in 1869)
They are something to do with atoms
Their properties were under intense investigation during the 1890s.
X-ray discovered by Röntgen in 1895, 1901 Nobel prize in physics

6. J. J. Thomson’s Cathode-Ray Experiment (1897)
Cathode rays – particles (Thomson) or wave (Hertz)?
Cathode rays were negatively charged particles
Discovery of electrons (1897)

7. Thomson’s experiment to determine e/m
Send electrons through a region containing a magnetic field perpendicular to an electric field
1906 Nobel prize

8. Calculation of e/m
An electron moving through the electric field is accelerated by a force:
Electron angle of deflection:
The magnetic field deflects the electron against the electric field force.
The magnetic field is adjusted until the net force is zero.
Charge to mass ratio:

9. 3.2: Determination of Electron Charge
Millikan oil drop experiment

10. Calculation of the oil drop charge
Used an electric field and gravity to suspend a charged oil drop
Magnitude of the charge on the oil drop
Mass is determined from Stokes’s relationship of the terminal velocity to the radius and density
Thousands of experiments showed that there is a basic quantized electron charge C

11. 3.3: Line Spectra
Chemical elements produce unique wavelengths of light when burned or excited in an electrical discharge.
Advances in grating technology key to the success (Henry Rowland)
Thousands of ruling lines per cm

12. Optical Spectrometer
Diffraction creates a line spectrum pattern of light bands and dark areas on the screen.
Wavelengths of these line spectra allow identification of the chemical elements and the composition of materials.

13. Balmer Series nm (where k = 3,4,5… and k > 2)
In 1885, Johann Balmer found an empirical formula for wavelength of the visible hydrogen line spectra in nm:
nm (where k = 3,4,5… and k > 2)

14. Rydberg Equation
As more scientists discovered emission lines at infrared and ultraviolet wavelengths, the Balmer series equation was extended to the Rydberg equation:
(n = 2)

15. 3.5: Blackbody Radiation

16. Equivalence of blackbody and hole on cavity
looks like
is equivalent to
Blackbody
Light that goes in through the hole never comes out
This is as if it is fully absorbed => blackbody
Hole = blackbody

17. Emission power from the hole & radiation energy in the cavity
This is what we can calculate
This is what we want to know
Radiation energy
density u(l,T)
Emission power density I(l,T)
I(l,T) = c u(l,T), where c is a geometrical factor (independent of l and T)
The blackbody radiation problem reduces to calculation of u(l,T)

18. Expected energy of a mode
There are light waves with different wave lengths
However, only standing wave-like modes are allowed in the cavity
Let’s focus on this particular mode (blue)…
Each mode is equivalent to a vibrating string
Or a pendulum (oscillator) = =
Wave length (l) or frequency (n) of the mode is fixed
However, the amplitude A can be varied
Energy of the mode is proportional to A2, E A2
Since A can be of any value, E is continuous

19. Mode & oscillator & mean energy
Mean energy (energy
expectation value) <E>?
E large
E ~ 0
Energy continuous, anywhere between 0 and infinity
Nature prefers lower energy
Boltzmann told us that the probability ratio between states with energy E1 and E2 is P1/P2=exp[-(E1-E2)/kBT]
Energy expectation
<E> = kBT (equi-partition theorem)
Energy E
Probability density p(E)

20. Counting # of modes ky kx The volume between k and k+dk is 4pk2dk
# of modes within the volume is (4pk2dk)/(p/L)3
Let us N(l)dl be the # of modes within l and l+dl
Then, N(l)dl = (4pk2dk)/(p/L)3 or N(l)=(4k2L3/p2)(dk/dl)
 N(l)=(16L3/l2)(2p/l2)=32pL3/l4

21. Rayleigh-Jeans Formula
I(l,T) = c u(l,T)
u(l,T) = (# of modes within l and l+dl) x (energy expectation of each mode) = N(l) x kBT
“The ultraviolet catastrophe”, one of the outstanding exceptions that classical physics could not explain.

22. Planck’s trick h = 6.6261 × 10−34 J·s
 Don’t like probability ‘density’ and integration
Energy E
Probability density p(E)
Energy E
Probability Pn(En)
To get the result for continuous energy, simply send h  0.
Planck found that h=finite fits the data!
h = × 10−34 J·s

23. 3.6: Photoelectric Effect

24. Experimental Results

25. 3.7: X-Ray Production
In a sense, an inverse process of photoelectric effect
An energetic electron passing through matter will radiate photons and lose kinetic energy  Bremsstrahlung,
The final energy of the electron determined from the conservation of energy is
There is maximum frequency (minimum wave length) for given electron kinetic energy

26. Inverse Photoelectric Effect
Duane-Hunt limit : the limit in the X-ray wave length
The photon wavelength depends only on the accelerating voltage and is the same for all targets.

27. Compton effect