The cloud chamber shows the tracks of cosmic rays

• A cloud chamber consists of a sealed environment containing a supersaturated vapor of water or alcohol.
• An energetic charged particle (for example, an alpha or beta particle) interacts with the gaseous mixture by knocking electrons off gas molecules via electrostatic forces during collisions, resulting in a trail of ionized gas particles.
• The resulting ions act as condensation centers around which a mist-like trail of small droplets form if the gas mixture is at the point of condensation. These droplets are visible as a “cloud” track that persists for several seconds while the droplets fall through the vapor.
• These tracks have characteristic shapes. For example, an alpha particle track is thick and straight, while a beta particle track is wispy and shows more evidence of deflections by collisions

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• 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
• 3.9 Pair Production and Annihilation

CHAPTER 3�The Experimental Basis of Quantum Physics

3.1: Discovery of the X Ray and the Electron

• X rays were discovered by Wilhelm Röntgen in 1895.
• Observed x rays emitted by cathode rays bombarding glass

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• Electrons were discovered by J. J. Thomson.
• Observed that cathode rays were charged particles

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Cathode Ray Experiments

• In the 1890s scientists and engineers were familiar with “cathode rays”. These rays were generated from one of the metal plates in an evacuated tube across which a large electric potential had been established.
• It was surmised that cathode rays had something to do with atoms.
• It was known that cathode rays could penetrate matter and their properties were under intense investigation during the 1890s.

Observation of X Rays

• Wilhelm Röntgen studied the effects of cathode rays passing through various materials. He noticed that a phosphorescent screen near the tube glowed during some of these experiments. These rays were unaffected by magnetic fields and penetrated materials more than cathode rays.
• He called them x rays and deduced that they were produced by the cathode rays bombarding the glass walls of his vacuum tube.

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Röntgen’s X Ray Tube

• Röntgen constructed an x-ray tube by allowing cathode rays to impact the glass wall of the tube and produced x rays. He used x rays to image the bones of a hand on a phosphorescent screen.

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Apparatus of Thomson’s Cathode-Ray Experiment

• Thomson used an evacuated cathode-ray tube to show that the cathode rays were negatively charged particles (electrons) by deflecting them in electric and magnetic fields.

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12. How did Thomson measure the charge to mass ratio of the electron?

a.He shot helium nuclei into gold foil to measure the nuclei scattering against electrons within.

b.He passed cathode rays through a magnetic field and measured the deflection.

c.He suspended a drop of oil between electrodes to measure the electric field from the electrons.

d. He measured very precisely a known quantity of hydrogen atoms and calculated the reduced mass ratio within each atom.

Thomson’s Experiment

• Thomson’s method of measuring the ratio of the electron’s charge to mass was to send electrons through a region containing a magnetic field perpendicular to an electric field.

Calculation of e/m

• An electron moving through the electric field is accelerated by a force:

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• Electron angle of deflection:

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• The magnetic field deflects the electron against the electric field force.

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• The magnetic field is adjusted until the net force is zero.

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• Charge to mass ratio:

Examble 3.1

q/m= 1,8x 10 ^11 C/kg

3.2: Determination of Electron Charge

Millikan oil drop experiment

Oil drop is in motion, either falling without E, or rising with E

Calculation of the oil drop charge(at rest)

• Used an electric field and gravity to suspend a charged oil drop

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• Magnitude of the charge on the oil drop

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• Mass is determined from Stokes’s relationship of the terminal velocity to the radius and density

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• Thousands of experiments showed that there is a basic quantized electron charge

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C

3.3: Line Spectra

• Chemical elements were observed to produce unique wavelengths of light when burned or excited in an electrical discharge.

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• Collimated light is passed through a diffraction grating with thousands of ruling lines per centimeter.
• The diffracted light is separated at an angle θ according to its wavelength λ by the equation:

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where d is the distance between rulings and n is an integer called the order number

Optical Spectrometer

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• 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.

a

l

lo.

Balmer Series

• In 1885, Johann Balmer found an empirical formula for wavelength of the visible hydrogen line spectra in nm:

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nm (where k = 3,4,5… and k > 2)

Rydberg Equation

• As more scientists discovered emission lines at infrared and ultraviolet wavelengths, the Balmer series equation was extended to the Rydberg equation:

(n =1, 2,3…)

Transitions in the Hydrogen Atom

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Lyman series

The atom will remain in the excited state for a short time before emitting a photon and returning to a lower stationary state. All hydrogen atoms exist in n = 1 (invisible).

Balmer series

When sunlight passes through the atmosphere, hydrogen atoms in water vapor absorb the wavelengths (visible).

3.4: Quantization

• Current theories predict that charges are quantized in units (quarks) of ±e/3 and ±2e/3, but quarks are not directly observed experimentally. The charges of particles that have been directly observed are quantized in units of ±e.
• The measured atomic weights are not continuous—they have only discrete values, which are close to integral multiples of a unit mass.

Molecules consist of integral number of atoms. Modes in a cavity are discrete

Light=electromagnetic radiation

3.5: Blackbody Radiation

• When matter is heated, it emits radiation.
• A blackbody is a cavity in a material that only emits thermal radiation. Incoming radiation is absorbed in the cavity.

• Blackbody radiation is theoretically interesting because the radiation properties of the blackbody are independent of the particular material. Physicists can study the properties of intensity versus wavelength at fixed temperatures.

A key hole is always black and a black body

Wien’s Displacement Law

• The intensity (λ, T) is the total power radiated per unit area per unit wavelength at a given temperature.
• Wien’s displacement law: The maximum of the distribution shifts to smaller wavelengths as the temperature is increased.

(where λ_max = wavelength of the peak)

Blacksmith formining a horse shoe

Problem 21. Calculate the maximum wavelength for blackbody radiation(a) liquid helium at 4.2 K (b)room temperature at 293 K,(c)a steel furnace at 2500 K,(d) a blue star at 9000 K

When do you have fever?

for body temperature of 100 F (37.8 C )

Problem 21. Calculate the maximum wavelength for blackbody radiation(a) liquid helium at 4.2 K (b)room temperature at 293 K,(c)a steel furnace at 2500 K,(d) a blue star at 9000 K

Stefan-Boltzmann Law

• The total power radiated increases with the temperature:

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• This is known as the Stefan-Boltzmann law, with the constant σ experimentally measured to be 5.6705 × 10⁻⁸ W / (m² · K⁴).

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• The emissivity є (є = 1 for an idealized blackbody) is simply the ratio of the emissive power of an object to that of an ideal blackbody and is always less than 1.

T1=900x2^1/4=1070 K

Problem 20

There is more energy radiated away than consumed by eating

(a) At what wavelength will the human body radiate the maximum radiation? (b) Estimate the total power radiated by a person of medium build (assume an area given by a cylinder of 175-cm height and 13-cm radius). (c) Using your answer to (b), compare the energy radiated by a person in one day with the en- ergy intake of a 2000-kcal diet

273 +37 (body temperature in C) = 310

Planck’s Radiation Law

• Planck assumed that the radiation in the cavity was emitted (and absorbed) by some sort of “oscillators” that were contained in the walls. He used Boltzman’s statistical methods to arrive at the following formula that fit the blackbody radiation data.

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• Planck made two modifications to the classical theory:
• The oscillators (of electromagnetic origin) can only have certain discrete energies determined by E_n = nhf, where n is an integer, f is the frequencyof the radiation, and h is called Planck’s constant. �h = 6.6261 × 10⁻³⁴ J·s.
• The oscillators can absorb or emit energy in discrete multiples of the fundamental quantum of energy given by

Planck’s radiation law

Summary of blackbody radiation

S

Summary: Blackbody radiation

The Rydberg equation is used to

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a. Determine the ratio of the electron charge to its mass

b. Calculate the wavelengths of different spectral lines of hydrogen

c. Measure the mass of the hydrogen atom

d. Calculate the wavelengths of different transitions in energy level of electrons in helium

Question form chapter 3 quiz

How did Planck modify the classical theory of blackbody radiation to correctly determine his radiation law?�� a.He found that the blackbody model was incorrect for purposes of theory� b.He accepted the Stefan-Boltzmann law� c.He assumed light was absorbed and emitted in quanta� d.He realized that the charge of the electron was not quantized� e.He proved the necessity of relativistic considerations

3.6: Photoelectric Effect

Methods of electron emission:

• Thermionic emission: Application of heat allows electrons to gain enough energy to escape.
• Secondary emission: The electron gains enough energy by transfer from another high-speed particle that strikes the material from outside.
• Field emission: A strong external electric field pulls the electron out of the material.
• Photoelectric effect: Incident light (electromagnetic radiation) shining on the material transfers energy to the electrons, allowing them to escape.

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Electromagnetic radiation interacts with electrons within metals and gives the electrons increased kinetic energy. Light can give electrons enough extra kinetic energy to allow them to escape. We call the ejected electrons photoelectrons.

Work function=minimum binding energy of the electron

In metals electrons are weakly bound in the conduction band

Experimental Setup

Experimental Results

threshold frequency

Same Kinetic energy

Frequency dependence of maximum kinetic energy

Stopping potential measures maximum kinetic energy

Work function

Photoelectric current starts in nsec

Experimental Results

1. The kinetic energies of the photoelectrons are independent of the light intensity.
2. The maximum kinetic energy of the photoelectrons, for a given emitting material, depends only on the frequency of the light.
3. The smaller the work function φ of the emitter material, the smaller is the threshold frequency of the light that can eject photoelectrons.
4. When the photoelectrons are produced, however, their number is proportional to the intensity of light.
5. The photoelectrons are emitted almost instantly following illumination of the photocathode, independent of the intensity of the light.

Classical Interpretation

• Classical theory predicts that the total amount of energy in a light wave increases as the light intensity increases.
• The maximum kinetic energy of the photoelectrons depends on the value of the light frequency f and not on the intensity.
• The existence of a threshold frequency is completely inexplicable in classical theory.
• Classical theory would predict that for extremely low light intensities, a long time would elapse before any one electron could obtain sufficient energy to escape. We observe, however, that the photoelectrons are ejected almost immediately.

Is not possible

Einstein’s Theory

• Einstein suggested that the electromagnetic radiation field is quantized into particles called photons. Each photon has the energy quantum:

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where f is the frequency of the light and h is Planck’s constant.

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• The photon travels at the speed of light in a vacuum, and its wavelength is given by

Einstein’s Theory

• Conservation of energy yields:

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where is the work function of the metal

Explicitly the energy is

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• The retarding potentials measured in the photoelectric effect are the opposing potentials needed to stop the most energetic electrons.

Quantum Interpretation

• The kinetic energy of the electron does not depend on the light intensity at all, but only on the light frequency and the work function of the material.

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• Einstein in 1905 predicted that the stopping potential was linearly proportional to the light frequency, with a slope h, the same constant found by Planck.

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• From this, Einstein concluded that light is a particle with energy:

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For Li

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Summary: photoelectric effect

A

An argument for solar power

Chapter 3, #57

A typical person can detect light with a minimum intensity of 4E-11 W/m2 . For light of this intensity and a wavelength of 550 nm, how many photons enter the eye each second if the pupil is open wide with a diameter of 9.0 mm?

Chapter 3, #58

A copper wire carrying a high current glows “red hot” just before the wire melts at a temperature of 1085C°

1. What is the peak wavelength of the emitted radiation?
2. Given your answer to part (a), how can the wire be “red hot”?

Problem 34. What is the threshold frequency for the photo electric effect in lithium with a work function of 2.93eV?What is the stopping potential if the wavelength of the incident light is 380 nm

When you increase only the intensity of the light onto the emitter, you measure

a. A decrease in the necessary stopping voltage

b. An increase in the necessary stopping voltage

c. No change in either current or stopping voltage

d. Either a or c. You cannot determine which from the information given.

e. An increased current

Question from chapter3 quiz

Maxwell classical light wave Einstein Photon particle

Rayleigh-jeans

Planck quantization

Einstein quantized photons

3.7: X-Ray Production(inverse photoelectric effect)

• An energetic electron passing through matter will radiate photons and lose kinetic energy which is called bremsstrahlung, from the German word for “braking radiation.” Since linear momentum must be conserved, the nucleus absorbs very little energy, and it is ignored. The final energy of the electron is determined from the conservation of energy to be

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• An electron that loses a large amount of energy will produce an X-ray photon. Current passing through a filament produces copious numbers of electrons by thermionic emission. These electrons are focused by the cathode structure into a beam and are accelerated by potential differences of thousands of volts until they impinge on a metal anode surface, producing x rays by bremsstrahlung as they stop in the anode material.

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Unlike the photon an electron can give up part of its energy(as bremsstrahlung) and be the same electron

bremsstrahlung, from the German word for “braking radiation “

What is the bremsstrahlung process?

a.The emission of a photon from an electron being accelerated by a nucleus

b.The emission of an electron from a metal when light is shined on it

c.Thermal excitation of photons in a substance

d.The emission of an electron from an inner electron shell and the resulting photon when an electron drops from an outer shell to take its place

e.Converting power-producing nuclear material to weapons grade

Inverse Photoelectric Effect.

• Conservation of energy requires that the electron kinetic energy equal the maximum photon energy where we neglect the work function because it is normally so small compared to the potential energy of the electron. This yields the Duane-Hunt limit which was first found experimentally. The photon wavelength depends only on the accelerating voltage and is the same for all targets.

m

Bremsstrahlung: in X-ray emission

3.8: Compton Effect

• When a photon enters matter, it is likely to interact with one of the atomic electrons. The photon is scattered from only one electron, rather than from all the electrons in the material, and the laws of conservation of energy and momentum apply as in any elastic collision between two particles. The momentum of a particle moving at the speed of light is

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• The electron energy can be written as

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• This yields the change in wavelength of the scattered photon which is known as the Compton effect:

Compton wavelength = h/mc = 2.426x 10^-3 nm

Figure 3-20 p114

Figure 3-21 p115

Thomson scattering=photon scattering from an tightly bound electron(use atom mass)

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Compton scattering=photon scattering from a loosely bound electron(use electron mass)

3.9: Pair Production and Annihilation

• If a photon can create an electron, it must also create a positive charge to balance charge conservation.
• In 1932, C. D. Anderson observed a positively charged electron (e⁺) in cosmic radiation. This particle, called a positron, had been predicted to exist several years earlier by P. A. M. Dirac.
• A photon’s energy can be converted entirely into an electron and a positron in a process called pair production.

Pair production from gamma ray

Cloud chamber with tracks left behind by positron and electron

Pair production

Pair annihilation

Conservation of mass energy

Proton – antiproton

Electron – positron

Hydrogen – antihydrogen

Neutron – antineutron

Matter – antimatter

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Pair Production in Empty Space

• Conservation of energy for pair production in empty space is

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• Considering momentum conservation yields

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• This energy exchange has the maximum value

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• Recall that the total energy for a particle can be written as

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However this yields a contradiction:

and hence the conversion of energy in empty space is an impossible situation.

Pair Production in Matter

• Since the relations and contradict each other, a photon can not produce an electron and a positron in empty space.
• In the presence of matter, the nucleus absorbs some energy and momentum.

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• The photon energy required for pair production in the presence of matter is

Pair Annihilation

• A positron passing through matter will likely annihilate with an electron. A positron is drawn to an electron by their mutual electric attraction, and the electron and positron then form an atomlike configuration called positronium.
• Pair annihilation in empty space will produce two photons to conserve momentum. Annihilation near a nucleus can result in a single photon.

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• Conservation of energy:

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• Conservation of momentum:

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• The two photons will be almost identical, so that

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• The two photons from positronium annihilation will move in opposite directions with an energy:

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Para-positronium T=0.12 ns,

Ortho-positronium T=138 ns

Exam 1 Grades

Exam 1 – Fall 2024

N = 255

Average = 82.6

A > 90

B > 80

C > 65

D > 55

F < 55