Chapter 27 Quantum Physics.

Chapter 27 Quantum Physics

Read and Take notes on Pages 596-601 in your Conceptual Physics Text

Need for Quantum Physics
Problems remained from classical mechanics that relativity didn’t explain. Blackbody Radiation The electromagnetic radiation emitted by a heated object Photoelectric Effect Emission of electrons by an illuminated metal Spectral Lines Emission of sharp spectral lines by gas atoms in an electric discharge tube Introduction

Development of Quantum Physics
Development of ideas of quantum mechanics Also called wave mechanics Highly successful in explaining the behavior of atoms, molecules, and nuclei Involved a large number of physicists Planck introduced basic ideas. Mathematical developments and interpretations involved such people as Einstein, Bohr, Schrödinger, de Broglie, Heisenberg, Born and Dirac. Introduction

(Start to minute 4:00 and 6:50 to end)
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Read and take notes on Pgs. 870-872 from College Physics text

Blackbody Radiation An object at any temperature emits electromagnetic radiation. Also called thermal radiation. Stefan’s Law describes the total power radiated. The spectrum of the radiation depends on the temperature and properties of the object. The spectrum shows a continuous distribution of wavelengths from infrared to ultaviolet. Section 27.1

Blackbody Radiation – Classical View
Thermal radiation originates from accelerated charged particles. Problem in explaining the observed energy distribution Opening in a cavity is a good approximation The nature of the radiation emitted through the opening depends only on the temperature of the cavity walls. Section 27.1

Blackbody Radiation Graph
Experimental data for distribution of energy in blackbody radiation As the temperature increases, the total amount of energy increases. Shown by the area under the curve As the temperature increases, the peak of the distribution shifts to shorter wavelengths. Section 27.1

Wien’s Displacement Law
The wavelength of the peak of the blackbody distribution was found to follow Wein’s Displacement Law. λmax T = x 10-2 m • K λmax is the wavelength at which the curve peaks. T is the absolute temperature of the object emitting the radiation. Section 27.1

The Ultraviolet Catastrophe
Classical theory did not match the experimental data. At long wavelengths, the match is good. At short wavelengths, classical theory predicted infinite energy. At short wavelengths, experiment showed no energy Section 27.1

Planck’s Resolution Planck hypothesized that the blackbody radiation was produced by resonators. Resonators were submicroscopic charged oscillators. The resonators could only have discrete energies. En = n h ƒ n is called the quantum number ƒ is the frequency of vibration h is Planck’s constant, x J s Key point is quantized energy states Section 27.1

Max Planck 1858 – 1947 Introduced a “quantum of action,” h
Awarded Nobel Prize in 1918 for discovering the quantized nature of energy Section 27.1

Quantized Energy Planck’s assumption of quantized energy states was a radical departure from classical mechanics. The fact that energy can assume only certain, discrete values is the single most important difference between quantum and classical theories. Classically, the energy can be in any one of a continuum of values. Section 27.1

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Pgs. 872-874 from College Physics text
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Photoelectric Effect When light is incident on certain metallic surfaces, electrons are emitted from the surface. This is called the photoelectric effect. The emitted electrons are called photoelectrons. The effect was first discovered by Hertz. The successful explanation of the effect was given by Einstein in 1905. Received Nobel Prize in 1921 for paper on electromagnetic radiation, of which the photoelectric effect was a part

Photoelectric Effect Schematic
When light strikes E, photoelectrons are emitted. Electrons collected at C and passing through the ammeter create a current in the circuit. C is maintained at a positive potential by the power supply. Section 27.2

Photoelectric Current/Voltage Graph
The current increases with intensity, but reaches a saturation level for large ΔV’s. No current flows for voltages less than or equal to –ΔVs, the stopping potential. Section 27.2

More About Photoelectric Effect
The stopping potential is independent of the radiation intensity. The maximum kinetic energy of the photoelectrons is related to the stopping potential: KEmax = eDVs Section 27.2

Features Not Explained by Classical Physics/Wave Theory
No electrons are emitted if the incident light frequency is below some cutoff frequency that is characteristic of the material being illuminated. The maximum kinetic energy of the photoelectrons is independent of the light intensity. Section 27.2

Light Quantum or Photons
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More Features Not Explained
The maximum kinetic energy of the photoelectrons increases with increasing light frequency. Electrons are emitted from the surface almost instantaneously, even at low intensities. Section 27.2

Einstein’s Explanation
A tiny packet of light energy, called a photon, would be emitted when a quantized oscillator jumped from one energy level to the next lower one. Extended Planck’s idea of quantization to electromagnetic radiation The photon’s energy would be E = hƒ Each photon can give all its energy to an electron in the metal. The maximum kinetic energy of the liberated photoelectron is KEmax = hƒ – φ φ is called the work function of the metal Section 27.2

Explanation of Classical “Problems”
The effect is not observed below a certain cutoff frequency since the photon energy must be greater than or equal to the work function. Without this, electrons are not emitted, regardless of the intensity of the light The maximum KE depends only on the frequency and the work function, not on the intensity. The absorption of a single photon is responsible for the electron’s kinetic energy. Section 27.2

More Explanations The maximum KE increases with increasing frequency.
The effect is instantaneous since there is a one-to-one interaction between the photon and the electron. Section 27.2

Verification of Einstein’s Theory
Experimental observations of a linear relationship between KE and frequency confirm Einstein’s theory. The x-intercept is the cutoff frequency. Section 27.2

Cutoff Wavelength The cutoff wavelength is related to the work function. Wavelengths greater than lC incident on a material with a work function f don’t result in the emission of photoelectrons. Section 27.2

X-Rays Discovered and named by Rӧntgen in 1895
Later identified as electromagnetic radiation with short wavelengths Wavelengths lower (frequencies higher) than for ultraviolet Wavelengths are typically about 0.1 nm. X-rays have the ability to penetrate most materials with relative ease. Section 27.3

Production of X-rays, 1 X-rays are produced when high-speed electrons are suddenly slowed down. Can be caused by the electron striking a metal target Heat generated by current in the filament causes electrons to be emitted. These freed electrons are accelerated toward a dense metal target. The target is held at a higher potential than the filament. Section 27.3

X-ray Spectrum The x-ray spectrum has two distinct components.
Continuous broad spectrum Depends on voltage applied to the tube Sometimes called bremsstrahlung The sharp, intense lines depend on the nature of the target material. Section 27.3

Production of X-rays, 2 An electron passes near a target nucleus.
The electron is deflected from its path by its attraction to the nucleus. This produces an acceleration It will emit electromagnetic radiation when it is accelerated. Section 27.3

Wavelengths Produced If the electron loses all of its energy in the collision, the initial energy of the electron is completely transformed into a photon. The wavelength can be found from Section 27.3

Wavelengths Produced, Cont.
Not all radiation produced is at this minimum wavelength. Many electrons undergo more than one collision before being stopped. This results in the continuous spectrum produced. Section 27.3

Arthur Holly Compton 1892 – 1962 Discovered the Compton effect
Worked with cosmic rays Director of the lab at U of Chicago Shared Nobel Prize in 1927 Section 27.5

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Pgs. 879 from College Physics text
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The Compton Effect Compton directed a beam of x-rays toward a block of graphite. He found that the scattered x-rays had a slightly longer wavelength that the incident x-rays. This means they also had less energy. The amount of energy reduction depended on the angle at which the x-rays were scattered. The change in wavelength is called the Compton shift. Section 27.5

Compton Scattering Compton assumed the photons acted like other particles in collisions. Energy and momentum were conserved. The shift in wavelength is Section 27.5

Compton Scattering, Final
The quantity h/mec is called the Compton wavelength. Compton wavelength = nm Very small compared to visible light The Compton shift depends on the scattering angle and not on the wavelength. Experiments confirm the results of Compton scattering and strongly support the photon concept. Section 27.5

Photons and Electromagnetic Waves
Light has a dual nature. It exhibits both wave and particle characteristics. Applies to all electromagnetic radiation Different frequencies allow one or the other characteristic to be more easily observed. The photoelectric effect and Compton scattering offer evidence for the particle nature of light. When light and matter interact, light behaves as if it were composed of particles. Interference and diffraction offer evidence of the wave nature of light. Section 27.6

Louis de Broglie 1892 – 1987 Discovered the wave nature of electrons
Awarded Nobel Prize in 1929 Section 27.6

Pgs. 880- 881 from College Physics text

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Wave Properties of Particles
In 1924, Louis de Broglie postulated that because photons have wave and particle characteristics, perhaps all forms of matter have both properties. Furthermore, the frequency and wavelength of matter waves can be determined. Section 27.6

de Broglie Wavelength and Frequency
The de Broglie wavelength of a particle is The frequency of matter waves is Section 27.6

Dual Nature of Matter The de Broglie equations show the dual nature of matter. Each contains matter concepts. Energy and momentum Each contains wave concepts. Wavelength and frequency Section 27.6

The Davisson-Germer Experiment
They scattered low-energy electrons from a nickel target. They followed this with extensive diffraction measurements from various materials. The wavelength of the electrons calculated from the diffraction data agreed with the expected de Broglie wavelength. This confirmed the wave nature of electrons. Section 27.6

The Electron Microscope
The electron microscope depends on the wave characteristics of electrons. Microscopes can only resolve details that are slightly smaller than the wavelength of the radiation used to illuminate the object. The electrons can be accelerated to high energies and have small wavelengths. Section 27.6

Werner Heisenberg 1901 – 1976 Developed an abstract mathematical model to explain wavelengths of spectral lines Called matrix mechanics Other contributions Uncertainty Principle Nobel Prize in 1932 Atomic and nuclear models Forms of molecular hydrogen Section 27.8

Chapter 28 Atomic Physics

Quantum Numbers and Atomic Structure
The characteristic wavelengths emitted by a hot gas can be understood using quantum numbers. No two electrons can have the same set of quantum numbers – helps us understand the arrangement of the periodic table. Atomic structure can be used to describe the production of x-rays and the operation of a laser. Introduction

Atomic Emissions Spectra
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Emission Spectra A gas at low pressure has a voltage applied to it.
The gas emits light which is characteristic of the gas. When the emitted light is analyzed with a spectrometer, a series of discrete bright lines is observed. Each line has a different wavelength and color. This series of lines is called an emission spectrum. Section 28.2

Examples of Emission Spectra
Section 28.2

Emission Spectrum of Hydrogen – Equation
The wavelengths of hydrogen’s spectral lines can be found from RH is the Rydberg constant RH = x 107 m-1 n is an integer, n = 1, 2, 3, … The spectral lines correspond to different values of n. Section 28.2

Spectral Lines of Hydrogen
The Balmer Series has lines whose wavelengths are given by the preceding equation. Examples of spectral lines n = 3, λ = nm n = 4, λ = nm Section 28.2

Absorption Spectra An element can also absorb light at specific wavelengths. An absorption spectrum can be obtained by passing a continuous radiation spectrum through a vapor of the element being analyzed. The absorption spectrum consists of a series of dark lines superimposed on the otherwise continuous spectrum. The dark lines of the absorption spectrum coincide with the bright lines of the emission spectrum. Section 28.2

Absorption Spectrum of Hydrogen
Section 28.2

Application of Absorption Spectrum
The continuous spectrum emitted by the Sun passes through the cooler gases of the Sun’s atmosphere. The various absorption lines can be used to identify elements in the solar atmosphere. Led to the discovery of helium Section 28.2

Specific Energy Levels
The lowest energy state is called the ground state. This corresponds to n = 1 Energy is –13.6 eV The next energy level has an energy of –3.40 eV. The energies can be compiled in an energy level diagram. Section 28.3

Specific Energy Levels, Cont.
The ionization energy is the energy needed to completely remove the electron from the atom. The ionization energy for hydrogen is 13.6 eV The uppermost level corresponds to E = 0 and n   Section 28.3

Energy Level Diagram Section 28.3

Atomic Transitions – Energy Levels
An atom may have many possible energy levels. At ordinary temperatures, most of the atoms in a sample are in the ground state. Only photons with energies corresponding to differences between energy levels can be absorbed. Section 28.7

Atomic Transitions – Stimulated Absorption
The blue dots represent electrons. When a photon with energy ΔE is absorbed, one electron jumps to a higher energy level. These higher levels are called excited states. ΔE = hƒ = E2 – E1 In general, ΔE can be the difference between any two energy levels. Section 28.7

Atomic Transitions – Spontaneous Emission
Once an atom is in an excited state, there is a constant probability that it will jump back to a lower state by emitting a photon. This process is called spontaneous emission. Typically, an atom will remain in an excited state for about 10-8 s Section 28.7

Atomic Transitions – Stimulated Emission
An atom is in an excited state and a photon is incident on it. The incoming photon increases the probability that the excited atom will return to the ground state. There are two emitted photons, the incident one and the emitted one. The emitted photon is exactly in phase with the incident photon. Section 28.7

Chapter 29 Nuclear Physics

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Nuclear Physics Topics in nuclear physics include
Properties and structure of atomic nuclei Radioactivity Nuclear reactions Decay processes Fission Fusion Introduction

Ernest Rutherford 1871 – 1937 Discovery that atoms could be broken apart Studied radioactivity Nobel prize in 1908 Section 29.1

Some Properties of Nuclei
All nuclei are composed of protons and neutrons. Exception is ordinary hydrogen with just a proton The atomic number, Z, equals the number of protons in the nucleus. The neutron number, N, is the number of neutrons in the nucleus. The mass number, A, is the number of nucleons in the nucleus. A = Z + N Nucleon is a generic term used to refer to either a proton or a neutron. The mass number is not the same as the mass. Section 29.1

Symbolism Symbol: Example:
X is the chemical symbol of the element. Example: Mass number is 27 Atomic number is 13 Contains 13 protons Contains 14 (27 – 13) neutrons The Z may be omitted since the element can be used to determine Z. Section 29.1

More Properties The nuclei of all atoms of a particular element must contain the same number of protons. They may contain varying numbers of neutrons. Isotopes of an element have the same Z but differing N and A values. Example, isotopes of carbon:

Charge The proton has a single positive charge, +e
The electron has a single negative charge, -e e = x C The neutron has no charge. Makes it difficult to detect Section 29.1

Mass It is convenient to use unified mass units, u, to express masses.
Based on definition that the mass of one atom of C-12 is exactly 12 u 1 u = x kg Mass can also be expressed in MeV/c2 From ER = m c2 1 u = MeV/c2 Section 29.1

Summary of Masses Section 29.1

The Size of the Nucleus First investigated by Rutherford in scattering experiments He found an expression for how close an alpha particle moving toward the nucleus can come before being turned around by the Coulomb force. The KE of the particle must be completely converted to PE. Section 29.1

Marie Curie 1867 – 1934 Discovered new radioactive elements
Shared Nobel Prize in physics in 1903 For study of radioactive substances Nobel Prize in Chemistry in 1911 For the discovery of radium and polonium Section 29.3

Radioactivity Radioactivity is the spontaneous emission of radiation.
Experiments suggested that radioactivity was the result of the decay, or disintegration, of unstable nuclei. Section 29.3

Radioactivity – Types Three types of radiation can be emitted
Alpha particles The particles are 4He nuclei. Beta particles The particles are either electrons or positrons. A positron is the antiparticle of the electron. It is similar to the electron except its charge is +e Gamma rays The “rays” are high energy photons. Section 29.3

Distinguishing Types of Radiation
A radioactive beam is directed into a region with a magnetic field. The gamma particles carry no charge and thus are not deflected. The alpha particles are deflected upward. The negative beta particles (electrons) are deflected downward. Positrons would be deflected upward. Section 29.3

Penetrating Ability of Particles
Alpha particles Barely penetrate a piece of paper Beta particles Can penetrate a few mm of aluminum Gamma rays Can penetrate several cm of lead Section 29.3

Pgs. 921-924, (exclude example problems) from College Physics text
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Alpha Decay When a nucleus emits an alpha particle it loses two protons and two neutrons. N decreases by 2 Z decreases by 2 A decreases by 4 Symbolically X is called the parent nucleus. Y is called the daughter nucleus. Section 29.4

Alpha Decay – Example Decay of 226 Ra
Half life for this decay is 1600 years Excess mass is converted into kinetic energy. Momentum of the two particles is equal and opposite. Section 29.4

Decay – General Rules When one element changes into another element, the process is called spontaneous decay or transmutation. The sum of the mass numbers, A, must be the same on both sides of the equation. The sum of the atomic numbers, Z, must be the same on both sides of the equation. Conservation of mass-energy and conservation of momentum must hold. Section 29.4

Nuclear Reactions Structure of nuclei can be changed by bombarding them with energetic particles. The changes are called nuclear reactions. As with nuclear decays, the atomic numbers and mass numbers must balance on both sides of the equation. Section 29.6

Nuclear Reactions – Example
Alpha particle colliding with nitrogen: Balancing the equation allows for the identification of X So the reaction is Section 29.6

Radiation Damage in Matter
Radiation absorbed by matter can cause damage. The degree and type of damage depend on many factors. Type and energy of the radiation Properties of the absorbing matter Radiation damage in biological organisms is primarily due to ionization effects in cells. Ionization disrupts the normal functioning of the cell. Section 29.7

Types of Damage Somatic damage is radiation damage to any cells except reproductive ones. Can lead to cancer at high radiation levels Can seriously alter the characteristics of specific organisms Genetic damage affects only reproductive cells. Can lead to defective offspring Section 29.7

Nuclear Energy and Elementary Particles
Chapter 30 Nuclear Energy and Elementary Particles

in your Conceptual Physics Text
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Processes of Nuclear Energy
Fission A nucleus of large mass number splits into two smaller nuclei Fusion Two light nuclei fuse to form a heavier nucleus Large amounts of energy are released in either case. Introduction

Forces and Particles Fundamental interactions govern the behavior of subatomic particles. The current theory of elementary particles states that all particles come from only two families Quarks Leptons Introduction

Nuclear Fission A heavy nucleus splits into two smaller nuclei.
The total mass of the products is less than the original mass of the heavy nucleus. Section 30.1

Fission Equation Fission of 235U by a slow (low energy) neutron
236U* is an intermediate, short-lived state Lasts about s X and Y are called fission fragments. Many combinations of X and Y satisfy the requirements of conservation of energy and charge. Section 30.1

More About Fission of 235U About 90 different daughter nuclei can be formed. Several neutrons are also produced in each fission event. Example: The fission fragments and the neutrons have a great deal of KE following the event. Section 30.1

Sequence of Events in Fission
The 235U nucleus captures a thermal (slow-moving) neutron. This capture results in the formation of 236U*, and the excess energy of this nucleus causes it to undergo violent oscillations. The 236U* nucleus becomes highly elongated, and the force of repulsion between the protons tends to increase the distortion. The nucleus splits into two fragments, emitting several neutrons in the process. Section 30.1

Sequence of Events in Fission – Diagram
Section 30.1

Chain Reaction Neutrons are emitted when 235U undergoes fission.
These neutrons are then available to trigger fission in other nuclei. This process is called a chain reaction. If uncontrolled, a violent explosion can occur. The principle behind the nuclear bomb, where 1 kg of 235U can release energy equal to about tons of TNT Section 30.1

Chain Reaction – Diagram
Section 30.1

Nuclear Reactor A nuclear reactor is a system designed to maintain a self-sustained chain reaction. The reproduction constant, K, is defined as the average number of neutrons from each fission event that will cause another fission event. The maximum value of K from uranium fission is 2.5. In practice, K is less than this A self-sustained reaction has K = 1 Section 30.1

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Nuclear Fusion Nuclear fusion occurs when two light nuclei combine to form a heavier nucleus. The mass of the final nucleus is less than the masses of the original nuclei. This loss of mass is accompanied by a release of energy. Section 30.2

Fusion in the Sun All stars generate energy through fusion.
The Sun, along with about 90% of other stars, fuses hydrogen. Some stars fuse heavier elements. Two conditions must be met before fusion can occur in a star. The temperature must be high enough. The density of the nuclei must be high enough to ensure a high rate of collisions. Section 30.2

Forces and Mediating Particles
Interaction (force) Mediating Field Particle Strong Gluon Electromagnetic Photon Weak W± and Z0 Gravitational Gravitons Section 30.3

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