Atomic Physics Chapter 28 Chapter 28

Atomic Models

Introduction How do neon signs work? How do neon signs work?

Our main focus will be on the hydrogen atom. Our main focus will be on the hydrogen atom.  It is the simplest atomic system.

Why is it important to study the hydrogen atom? Why is it important to study the hydrogen atom?  Studying the quantum numbers for the allowed states of hydrogen will help us to describe the allowed states of more complex atoms.  The hydrogen atom is an ideal system for relating theory to experimentation.  Much that we learn about hydrogen can be extended to single electron ions like He and Li.

Early Models Of The Atom The Greek model The Greek model  Tiny, hard, indestructible sphere 3

The J. J. Thomson model The J. J. Thomson model  A volume of positive charge is embedded with negative charges called “electrons”

The Rutherford model The Rutherford model  A positive nucleus orbited by electrons.  The nucleus contains 99.9% of the atom’s mass

The Rutherford model The Rutherford model  Which force holds the electrons in orbit?  The Coulomb force

Problems with the Rutherford Model There were two basic difficulties with the Rutherford model. There were two basic difficulties with the Rutherford model.  It could not explain why atoms radiate discrete frequencies.  Accelerating electrons should radiate electromagnetic waves.

Electron Transitions Using a high voltage to move electrons through a gas causes the gas electrons to become excited and to jump from lower energy levels to higher energy levels. Using a high voltage to move electrons through a gas causes the gas electrons to become excited and to jump from lower energy levels to higher energy levels. Photons of various wavelengths are produced when electrons fall from higher energy levels to lower energy levels. Photons of various wavelengths are produced when electrons fall from higher energy levels to lower energy levels.

Emission Spectra The emission spectrum of hydrogen The emission spectrum of hydrogen  Can be produced by applying a high voltage across an evacuated glass tube filled with hydrogen  The observed wavelengths are characteristic only of hydrogen 279, 57

The Balmer Series In the Balmer Series In the Balmer Series  n f = 2  There are four prominent wavelengths  nm (red)  nm (green)  nm (purple)  nm (deep violet) 278, 28.7

Balmer Wavelengths

The Balmer Series Wavelength Equation  R H is the Rydberg constant R H = x 10 7 m -1

Two Other Important Series Lyman series (UV) Lyman series (UV)  n f = 1 Paschen series (IR) Paschen series (IR)  n f = 3 70

Spectral Lines How many different spectral lines could be produced by an electron in the n = 3 state? How many different spectral lines could be produced by an electron in the n = 3 state? Three Three

How many different spectral lines could be produced by an electron in the n = 4 state? How many different spectral lines could be produced by an electron in the n = 4 state? Six Six

Photon Energy The equation for determining the energy of the emitted photon in any series: The equation for determining the energy of the emitted photon in any series:

The Absorption Spectrum An element can absorb the same wavelengths that it emits. An element can absorb the same wavelengths that it emits. The spectrum consists of a series of dark lines. The spectrum consists of a series of dark lines.

Identifying Elements The absorption spectrum was used to identify elements in the solar atmosphere were identified in this way. The absorption spectrum was used to identify elements in the solar atmosphere were identified in this way.  Helium was discovered.

Thermal vs. Atomic Spectra How could you tell if the light from a candle flame is thermal or atomic in origin? How could you tell if the light from a candle flame is thermal or atomic in origin?

If the spectrum is continuous, the source must be thermal. If the spectrum is continuous, the source must be thermal.

Auroras What is the origin of the colors in the aurora borealis? What is the origin of the colors in the aurora borealis?

High speed particles from space interact with the earth’s magnetic field. High speed particles from space interact with the earth’s magnetic field.

The Bohr Theory Of Hydrogen At the beginning of the 20 th century, scientists wondered why atoms only radiated certain wavelengths. At the beginning of the 20 th century, scientists wondered why atoms only radiated certain wavelengths.  Bohr provided an explanation.

Four Assumptions of The Bohr Theory 1) The electron orbits the proton due to the 1) The electron orbits the proton due to the Coulomb force which produces centripetal Coulomb force which produces centripetal acceleration. acceleration.

2) Only certain electron orbits are stable 2) Only certain electron orbits are stable and do not radiate energy. and do not radiate energy.

3) Radiation is only emitted when an 3) Radiation is only emitted when an electron drops from a more energetic electron drops from a more energetic state to a lower state. state to a lower state.

4) The radius of the electron’s orbit is 4) The radius of the electron’s orbit is determined by the electron’s orbital determined by the electron’s orbital angular momentum. angular momentum.28.6

Total Energy of the Hydrogen Atom  The total energy of the hydrogen atom can be determined by using this equation.

The Bohr Radius An electron can exist only in certain allowed orbits determined by the integer n. An electron can exist only in certain allowed orbits determined by the integer n.  When n = 1, we have what is known as the Bohr radius (a o ). a o = nm a o = nm

Orbital Radii  A general equation for finding the radius of any orbit:

Energy States  The energy for various energy states can be found by using: n= 1 is the ground state n= 1 is the ground state

Ionization Energy  The minimum energy required to ionize the atom is called the ionization energy.  An electron is completely removed from the atom.

The Hydrogen Spectrum  The general expression for determining wavelengths of the various series in the hydrogen spectrum

Bohr’s Correspondence Principle Quantum mechanics is in agreement with classical physics when the energy differences between quantized levels are very small. Quantum mechanics is in agreement with classical physics when the energy differences between quantized levels are very small.

Successes of the Bohr Theory It accounted for the Balmer series and other series. It accounted for the Balmer series and other series.

It predicted a value for the Rydberg constant that agreed strongly with the experimental value. It predicted a value for the Rydberg constant that agreed strongly with the experimental value.

It gave an expression for the radius of the hydrogen atom. It gave an expression for the radius of the hydrogen atom.

It predicted the energy levels of hydrogen. It predicted the energy levels of hydrogen.

It also works with hydrogen-like (one electron) atoms. It also works with hydrogen-like (one electron) atoms.  Singly ionized helium

It also works with hydrogen-like (one electron) atoms. It also works with hydrogen-like (one electron) atoms.  Doubly ionized lithium

It also works with hydrogen-like (one electron) atoms. It also works with hydrogen-like (one electron) atoms.  Triply ionized beryllium

Four Quantum Numbers The state of an electron is specified by four quantum numbers. The state of an electron is specified by four quantum numbers.  These numbers describe all possible electron states.  The total number of electrons in a particular energy level is given by:

Principle Quantum Number The principal quantum number (n) where n = 1, 2, 3, … The principal quantum number (n) where n = 1, 2, 3, …  Determines the energy of the allowed states of hydrogen  States with the same principal quantum number are said to form a shell  K, L, M, … (n = 1, 2, 3, …)

Orbital Quantum Number The orbital quantum number ( l ) where l ranges from 0 to (n – 1) in integral steps The orbital quantum number ( l ) where l ranges from 0 to (n – 1) in integral steps  Allows multiple orbits within the same energy level  Determines the shape of the orbits  States with given values of n and l are called subshells  s ( l = 0), p ( l = 1), d ( l = 2), f ( l = 3), etc…

Electron Subshells

Generally, the electrons in the s subshell are at the lowest energy level and those in the f subshell in the highest shell occupy the highest energy level. Generally, the electrons in the s subshell are at the lowest energy level and those in the f subshell in the highest shell occupy the highest energy level.

As the shell number (n) increases the energy difference between the shells diminishes, as shown by the decreasing distance between each successive shell. As the shell number (n) increases the energy difference between the shells diminishes, as shown by the decreasing distance between each successive shell.

Electron Subshells

Magnetic Quantum Number The magnetic quantum number (m l ) where m l ranges from - l to + l in integral steps The magnetic quantum number (m l ) where m l ranges from - l to + l in integral steps  Explains why strong magnetic fields can cause single spectral lines to split into several closely spaced lines  Called the Zeeman effect

Spin Magnetic Quantum Number The spin magnetic quantum number (m s ) where m s can only be or – 0.5 The spin magnetic quantum number (m s ) where m s can only be or – 0.5  Accounts for the fine structure of “single” spectral lines in the absence of a magnetic field

Hydrogen Like Atoms Two important equations for hydrogen-like atoms: Two important equations for hydrogen-like atoms:  Orbital energy  Orbital radius

Angular Momentum Physicists agreed that angular momentum was quantized but no one was able to explain why. Physicists agreed that angular momentum was quantized but no one was able to explain why.28.10

Electron Standing Waves de Broglie stated that an electron orbit would be stable if it contained an integral number of electron wavelengths. de Broglie stated that an electron orbit would be stable if it contained an integral number of electron wavelengths.  Analogous to standing waves in a string

Wave Properties It became generally agreed upon that wave properties were involved in the behavior of atomic systems. It became generally agreed upon that wave properties were involved in the behavior of atomic systems.

Quantum Mechanics And The Hydrogen Atom A review of the various quantum number ranges which are used to determine allowable states A review of the various quantum number ranges which are used to determine allowable states  n can range from 1 to infinity in integral steps  l can range from 0 to (n - 1) in integral steps  m l can range from – l to + l in integral steps  m s can only be + ½ or – ½

The Spin Magnetic Quantum Number The spin magnetic quantum number explains the splitting of each energy level into two (the Zeeman Effect). The spin magnetic quantum number explains the splitting of each energy level into two (the Zeeman Effect).  It explains how two very closely spaced lines may be formed in the spectra of certain gases.  Electron spin (spin-up and spin-down)

Questions 2, 8, 12 Pg. 910

Electron Clouds The electron may be found at various distances from the nucleus but the probability of finding it at a distance corresponding to the first Bohr orbit is a maximum. The electron may be found at various distances from the nucleus but the probability of finding it at a distance corresponding to the first Bohr orbit is a maximum.  It can be found in a spherical region known as the “electron cloud”. 281, , 282

The State of an Electron The state of an electron is specified by four quantum numbers. The state of an electron is specified by four quantum numbers.  These numbers describe all possible electron states.  The total number of electrons in a particular energy level is given by:

The Pauli Exclusion Principle Two electrons in an atom can never have the same set of quantum numbers. Two electrons in an atom can never have the same set of quantum numbers.  Because of this, the elements all have different chemical properties.  The n = 1 energy level is filled with electrons first.

The Pauli Exclusion Principle And The Periodic Table Mendeleev arranged the elements in a periodic table according to their atomic masses and chemical similarities. Mendeleev arranged the elements in a periodic table according to their atomic masses and chemical similarities.  He left gaps which were filled in within the next 20 years.  Vertical columns have similar chemical properties. 15

The Periodic Table

Special Groups Within the Periodic Table Noble gases Noble gases  The outer shell is filled. Alkali metals Alkali metals  The outer shell has only one electron. Halogens Halogens  The outer shell needs one electron.

The Dow Corning Periodic Table

X-Rays X-rays are emitted when a metal target is bombarded with high-energy electrons to produce: X-rays are emitted when a metal target is bombarded with high-energy electrons to produce:  A broad continuous band  Bremsstrahlung  Characteristic x-rays  K  and K  284, 285

X-Ray Photons What can the incoming electron from an electron gun do to a K-shell electron in a tungsten target atom? What can the incoming electron from an electron gun do to a K-shell electron in a tungsten target atom?  It can knock a K-shell electron out of its energy level. Then, an electron from a higher energy level can fall into the K-shell (n = 1).  The energy lost by the falling electron shows up as an emitted x-ray photon.

Characteristic X-Rays K-shell emission produces higher-intensity x-rays than Bremsstrahlung. K-shell emission produces higher-intensity x-rays than Bremsstrahlung. The x-ray photon comes out at a single (characteristic) wavelength. The x-ray photon comes out at a single (characteristic) wavelength.  K  or K 

K  X-Rays When an incoming electron forces an electron out of the K shell an electron can drop down from the n = 2 level and a K  x-ray photon is emitted. When an incoming electron forces an electron out of the K shell an electron can drop down from the n = 2 level and a K  x-ray photon is emitted.

K  X-Rays When an incoming electron forces an electron out of the K shell an electron can drop down from the n = 3 level and a K  x-ray photon is emitted. When an incoming electron forces an electron out of the K shell an electron can drop down from the n = 3 level and a K  x-ray photon is emitted.

Which x-ray photon has the highest energy? Which x-ray photon has the highest energy?

K  X-Ray Wavelengths The wavelength of the emitted K  x-ray photon is given by: The wavelength of the emitted K  x-ray photon is given by:

Electron Shielding One electron in the K shell partially shields the other from the charge of the nucleus. One electron in the K shell partially shields the other from the charge of the nucleus.  Because of this, we use Z eff = (Z - 1) in the K  equation.

K  X-Ray Wavelengths The wavelength of the emitted K  x-ray photon is given by: The wavelength of the emitted K  x-ray photon is given by:

Electron Shielding One electron in the K shell and eight electrons in the L shell partially shield the M-shell electrons from the charge of the nucleus. One electron in the K shell and eight electrons in the L shell partially shield the M-shell electrons from the charge of the nucleus.  Because of this, we use Z eff = (Z - 9) in the K  equation.

Atomic Transitions Atoms will only emit or absorb EM radiation at certain frequencies corresponding to transitions involving the various energy states. Atoms will only emit or absorb EM radiation at certain frequencies corresponding to transitions involving the various energy states.

Stimulated Absorption In the stimulated absorption process, light may be used to stimulate electrons to higher excited states. In the stimulated absorption process, light may be used to stimulate electrons to higher excited states.  Only certain frequencies will do this

Spontaneous Emission When the electrons randomly fall back to their original orbits we call this spontaneous emission. When the electrons randomly fall back to their original orbits we call this spontaneous emission

Spontaneous Emission

Stimulated Emission In stimulated emission, all of the electrons can be made to fall back at the same time and thus produce bright, coherent light. In stimulated emission, all of the electrons can be made to fall back at the same time and thus produce bright, coherent light.  This is the basis for the operation of LASERS.

Stimulated Emission

Lasers LASER - L ight Amplification by S timulated E mission of R adiation LASER - L ight Amplification by S timulated E mission of R adiation

Population Inversion In a laser, electrons are stimulated so that there are more electrons in the excited state than in the ground state. In a laser, electrons are stimulated so that there are more electrons in the excited state than in the ground state.  This is called a population inversion. 287

Laser Requirements There are three conditions for laser action to occur. There are three conditions for laser action to occur.  A population inversion  The excited state must be a metastable (long lifetime) state.  The photons must be confined long enough to stimulate further emissions.

He-Ne Lasers The operation of a He-Ne laser The operation of a He-Ne laser  An oscillator is used to sweep electrons through a thin glass tube containing a He-Ne mixture.  The neon atoms are raised to a metastable state by collisions with excited helium atoms.  Electrons simultaneously returning to a lower energy state emit coherent photons of a particular wavelength. (632.8 nm) 28.22a, 71, 288

Laser Frequencies Frequency ranges of lasers Frequency ranges of lasers  Infrared (CO 2 )  Visible (red, green, blue)  Ultraviolet

Laser Applications Medical Medical  “Welding” detached retinas  Laser surgery  Laser vision correction (Lasik)

Lasik Surgery An ultra-thin flap is created on the eye's surface during LASIK corrective eye surgery. After laser energy is applied to reshape the eye, the flap is replaced to serve as a type of natural bandage. An ultra-thin flap is created on the eye's surface during LASIK corrective eye surgery. After laser energy is applied to reshape the eye, the flap is replaced to serve as a type of natural bandage.

Surveying and distance measurement Surveying and distance measurement

Cutting and drilling metals in industry Cutting and drilling metals in industry

Fiber optic communications Fiber optic communications

Holography Used in the production of three-dimensional images Used in the production of three-dimensional images Interference patterns are placed on film. Interference patterns are placed on film. Used to protect credit cards Used to protect credit cards 283, 284

Making Holograms

CDs and DVDs Information is stored in binary form. Information is stored in binary form.  Pits and land areas (ones and zeros) The laser beam follows a spiral path. The laser beam follows a spiral path. A diffraction grating is used to provide tracking. A diffraction grating is used to provide tracking. 40+ second memory for music CDs 40+ second memory for music CDs

Infrared Remote Control A different infrared wavelength is assigned to each number or function. A different infrared wavelength is assigned to each number or function.  TV and stereo remote controls use IR.  Some computers and calculators use IR.  My MAC PowerPoint remote uses RF. Don’t confuse IR with RF controls. Don’t confuse IR with RF controls. MAC Photo Booth Demo MAC Photo Booth Demo

Semiconductor Devices Doping Doping  Donor atoms  N-type semiconductor  Acceptor atoms  P-type semiconductors

Semiconductor Devices P-N junctions P-N junctions  Diodes  Forward bias  Reverse bias  Half-wave rectifiers  Full-wave rectifiers  Transistors

Transistors Junction transistors Junction transistors  Types  npn  pnp  Parts of a transistor  Emitter  Base  Collector 227

Semiconductor Devices Integrated circuits Integrated circuits  What are they?  Where are they used?  What are the advantages of integrated circuits?

Computer Memory

Questions 7, , 15 Pg. 910