Quantum Physics Chapter 27

Introduction What is a “quantum”? The special theory of relativity did not answer all questions about matter. Blackbody radiation? Photoelectric effect? Spectral lines from gas discharge tubes?

Between 1900 and 1930 quantum mechanics was developed to help explain the behavior of atoms, molecules, and nuclei. It modifies our ideas concerning the physical world.

Famous scientists involved in the development of the quantum theory: Einstein Bohr Schrodinger de Broglie Heisenberg Born Dirac

We will discuss: The photoelectric effect The Compton effect X-rays

Blackbody Radiation And Planck’s Hypothesis Thermal radiation Emitted by an object at any temperature The radiated spectrum depends upon the temperature and other properties of the object. Incandescent light bulb demonstration It is produced by accelerating charged particles near the surface of the object.

What is a blackbody?

Blackbody Radiation What is a blackbody? It is an ideal system that absorbs all radiation incident upon it. It is also a perfect emitter of radiation as a function of temperature.

When the temperature of a blackbody increases: The total maximum intensity of the emitted radiation increases The peak of the energy distribution shifts toward the shorter wavelengths (higher frequencies). 27.2, 27.3

Blackbody Radiation

Wien’s displacement law T is the absolute temperature. It can be used to determine the temperature of objects by measuring their peak emitted wavelength Finding the temperature of stars

Planck’s Hypothesis Planck Developed a better equation for predicting blackbody radiation This overcame the weaknesses of the Wien displacement law. Originated the concept of submicroscopic electric oscillators (resonators)

Planck’s first assumption The resonators could only have discrete amounts of energy (En) given by n is a positive integer called the principle quantum number h = 6.626 x 10-34 J.s

Planck’s second assumption The resonators emit discrete units of light that are called photons.

Electron Transitions Electrons jump from one quantum state (energy level) to another.

Photon Energy Equation for the energy of a photon 274

The electron will absorb or radiate energy only when it changes quantum states.

Plank’s Theory The key point of Planck’s theory is the radical assumption of quantized energy states. This development marked the birth of the quantum theory. Most scientists (including Planck!) didn’t consider the quantum to be realistic.

The Photoelectric Effect When light is incident upon certain metallic surfaces, electrons are emitted from the surfaces. (Figure 27.5) This is called the photoelectric effect. The emitted electrons are called photoelectrons. It was first discovered by Hertz. 275

Important concepts involving the photoelectric effect: Stopping potential (DV) A negative potential can stop the electrons. Cutoff frequency (fc) No electrons are emitted for incident light below this frequency. Inconsistent with the wave theory 27.4

Other important concepts: The maximum KE of the photoelectrons is independent of light intensity. The maximum KE of the photoelectrons increases with increasing light frequency. Electrons are emitted from the surface almost instantaneously. 27.4

Einstein received the Nobel Prize in 1921 for successfully explaining the photoelectric effect in 1905. He said that all electromagnetic waves can be considered as a stream of photons. Each photon has a discrete energy E.

Einstein’s view: A photon can give up all of its energy (hf) to a single electron in the metal. Electrons emitted from the surface of the metal possess KE.

The Work Function f is called the work function of the metal. It represents the minimum energy (in eV) needed to free an electron from the metal.

Photoelectric effects: No emission occurs below the cutoff frequency and the KE increases with frequency. KEmax is independent of the intensity of the light. Doubling the light intensity doubles the number of electrons emitted. 27.5, 38-1,

Photoelectric Effect Animation

Cutoff Wavelength The equation for cutoff wavelength: There is no emission for wavelengths greater than lc

Photocells What are they? How do they work?

Uses for the photoelectric cell: Sound tracks on motion picture film Used to control outdoor lights Garage door safety Elevator safety Analyzing bacterial growth Used in “Breathalyzers” 272

X-Rays Accidentally discovered in 1895 by Wilhelm Roentgen while he was studying electrical discharges in low pressure gases. The nature of the mysterious radiation was unknown, thus the name x-rays. They traveled at the speed of light. They were unaffected by electric or magnetic fields. They were not a beam of charged particles.

The formation of x-rays is like an inverse photoelectric effect.

X-ray photons are produced when high speed electrons are suddenly decelerated. Electrons striking a metal target is one method. X-ray tubes 27.8

The x-ray spectrum Two distinct features Broad continuous spectrum Bremsstrahlung (braking radiation) A number of sharp lines Characteristic x-rays

The shortest wavelength x-radiation that can be produced is given by

Characteristics of X-Rays Extremely penetrating Can produce burns Can cause cancer

X-Ray Applications Fluoroscopes were widely used in shoe stores between 1930 and 1960 to check the bones of the foot. Abandoned because of health risks

A lead apron is used in dental offices to protect patients during dental x-rays .

Dental X-Rays

X-rays are also used to examine paintings for authenticity.

Diffraction of X-Rays by Crystals Max von Laue suggested the possibility of using crystals as a diffraction grating to diffract the x-rays. Their wavelength could now be determined. It is about 0.10 nm 27.11

Diffraction gratings cannot be used with x-rays because the slits are much too wide. Crystals work well because the spacing between the atoms acts like a 3-dimensional grating. Sodium chloride crystals may be used. A Laue diffraction pattern is observed.

Bragg’s Law The condition for constructive interference is given by Bragg’s law. Bragg and his son shared a Nobel Prize in 1915.

Questions 1 - 3, 5, 7, 8, 10 - 13 Pg. 888

The Compton Effect Compton directed a beam of x-rays at a block of graphite. The scattered x-rays had a slightly longer wavelength than the incident x-rays. This meant that the scattered x-rays had a lower energy. 276, 27.18

The Compton Effect The change in wavelength (Dl) is called the Compton shift. The Compton effect demonstrated that photons behave like particles.

The Compton Effect The Compton shift is given by (h/mec) is called the Compton wavelength 27.16

The Compton Effect (h/mec) = 0.00243 nm (h/mec) is called the Compton wavelength (h/mec) = 0.00243 nm

The Compton Effect The Compton shift depends upon the scattering angle but not upon the wavelength.

The Compton Effect The photoelectric effect and the Compton effect both involve the loss or gain of kinetic energy. Photons lose energy Electrons gain KE.

Pair Production And Pair Annihilation Can a photon produce a single charged particle?

Pair Production And Pair Annihilation In pair production, a photon is converted completely into mass. Electron-positron pairs can be formed. What is a positron?

Photons And Electromagnetic Waves Light has a dual nature. It has the properties of both waves and particles. The wave nature is difficult to detect at high frequencies. The particle nature is difficult to detect at low frequencies.

The Wave Properties Of Particles Light has a dual nature but particles can also exhibit wave properties. Matter has a dual nature as well.

The Wave Properties Of Particles de Broglie postulated that because photons have wave and particle characteristics, perhaps all forms of matter have a dual nature. A highly revolutionary idea He said that electrons have wave properties.

The Wave Properties Of Particles Equation for the momentum of a photon

The Wave Properties Of Particles Equation for the de Broglie wavelength of a particle

The Wave Properties Of Particles Both equations have wave and particle characteristics.

The Wave Properties Of Particles Davisson and Germer accidentally discovered that electrons can exhibit diffraction. They confirmed de Broglie’s prediction. 274, 25-6

The Wave Properties Of Particles Application: The Electron Microscope It relies on the wave characteristics of electrons. It has a much greater resolving power. High energy electrons have very short wavelengths. All microscopes detect details close in size to the wavelength being used. Resolution is 100x better than light microscopes.

The Wave Function The Schrodinger equation: Described the manner in which waves change in space and time Is a key element in the theory of quantum mechanics Is as important in quantum mechanics as Newton’s laws are in classical mechanics Deals with the probability of finding a particle in a particular location

The Uncertainty Principle Quantum theory predicts that it is impossible to make simultaneous measurements of a particle’s position and velocity with infinite accuracy. This is called the Heisenberg uncertainty principle.

The Uncertainty Principle If Dx is made very small, Dpx will be large and vice versa. Position and momentum cannot both be measured with accuracy simultaneously. 277, 278

The Uncertainty Principle The measuring procedure itself limits the accuracy of the measurements.

The Uncertainty Principle The uncertainty principle also states that It is also impossible to simultaneously measure the energy of a particle in an infinitely short interval of time

The Uncertainty Principle Experiments designed to reveal the wave character of an electron will diminish its particle character.

The Uncertainty Principle Experiments designed to reveal the particle character of an electron will diminish its wave character.

The Uncertainty Principle The Heisenberg uncertainty principle predicts that all molecular motion will not cease at absolute zero.

The Uncertainty Principle

The Scanning Tunneling Microscope We are able to view single atoms. Distances as small as 0.20 nm can be discerned. Optical microscopes can only resolve objects in the 200 nm range.

The Scanning Tunneling Microscope

The Scanning Tunneling Microscope It’s operation is based upon the concept of “tunneling” which was understood in the 1920s but the microscope wasn’t built until the 1980s when the technology became available.

The Scanning Tunneling Microscope The scanning tunneling microscope (STM) is being replaced by the atomic force microscope (AFM).

Questions 4, 6, 14 Pg. 888