Atomic Physics

1
Atomic Physics

• Quantization of Energy
• Atomic Models
• Quantum Mechanics

2
Electric and Magnetic FieldsSummary

• A changing magnetic field can induce a current in
  a circuit (Faradays Law of Induction)
• A magnetic field is created around a
  current-carrying wire (Amperes Law)
• Electric field lines start on positive charges
  and end at negative charges (Coulombs Law /
  Gausss Law)
• Magnetic field lines always form closed loops
  with no beginning and no end (Gausss Law for
  magnetism)
• These unrelated observations, experiments and
  equations were all known by the mid-1800s, but
  nothing linked them together.

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Maxwells Equations

• James Clerk Maxwell (1831-1879)
• Scottish theoretical physicist mathematician
• Maxwells Equations
• Set of differential equations that describe the
  relationship between electric and magnetic field
• Summarized all previous work of Coulomb, Ampere,
  Gauss, Faraday others

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Maxwells Equations
Relax!!! You dont need to use these.
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Maxwells Equations

• Predicted
• a changing magnetic field would create a changing
  electric field, which would, in turn, create a
  changing magnetic field, and so on
• existence of electromagnetic waves that move
  through space at the speed of light
• light is an electromagnetic wave
• Confirmed
• Heinrich Hertz in 1887
• generated and detected the first E/M waves

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Electromagnetic Waves

• Oscillating electric and magnetic fields
• E-field and B-field are at right angles to each
  other
• Propagates at a right angle to both fields
  (transverse wave)

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Electromagnetic Waves

• EM waves can be produced most easily by an
  oscillating charged particle
• Frequency of oscillation determines frequency of
  the EM wave
• Wavelength related to frequency by

8
Electromagnetic Radiation

• Energy is the ability to do work
• E-fields B-fields store energy because they
  exert a force (do work) on charged particles
• Electromagnetic Radiation
• transfer of energy associated with electric and
  magnetic fields
• can be transferred to objects in the EM waves
  path
• can be converted to other forms, such as heat
• Continuous distribution of wavelengths on the
  electromagnetic spectrum.

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Electromagnetic Spectrum
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Blackbody Radiation

• All objects emit electromagnetic radiation
• Continuous distribution of wavelengths from the
  infrared, visible, and UV portions of the EM
  spectrum
• Intensity distribution of different wavelengths
  varies with temperature
• At low temps mostly infrared (invisible)
• Temp increases distribution shifts to visible
  UV
• Metals glow red gt yellow gt white gt blue

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Blackbody Radiation

• Most objects absorb some incoming radiation and
  reflect the rest
• Blackbody
• Ideal system that absorbs all incoming radiation
• Hollow object with a small opening
• Perfect absorber and perfect radiator
• Emits radiation based only on its temperature
• In 1900, Max Planck (1858-1947), proposed that
  the walls of a blackbody contained billions of
  submicroscopic electric oscillators, which he
  called resonators. These resonators, produced the
  blackbody radiation.

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Blackbody Radiation
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Quantization of Energy

• Planck found that the total energy of a resonator
  is an integer multiple of the frequency
• Because the energy of each resonator comes in
  discrete units, it is said to be quantized.
• Allowed energy states are called quantum states
  or energy levels.
• Einstein applied the concept of quantized energy
  to light.
• Photon quantized unit of light energy
• Photons are absorbed or given off by electrons
  jumping from one quantum state to another.

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Quantization of Energy
15
The Photoelectric Effect
When light strikes a metal surface, the surface
may emit electrons, called photoelectrons.

• Classical physics predicts
• Light waves of any frequency should have enough
  energy to eject electrons if the intensity is
  high enough
• At low intensities, electrons should be ejected
  if light shines on the metal for a long enough
  period of time
• Increasing the intensity of the light waves
  should increase the kinetic energy of the
  photoelectrons.
• Maximum kinetic energy of a photoelectron should
  be determined by the lights intensity

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The Photoelectric Effect

• Experimental evidence shows that
• No photoelectrons emitted if the light frequency
  falls below a certain threshold frequency, even
  if the intensity is very high
• Threshold frequency, ft, depends on material
• If light frequency exceeds ft
• of photoelectrons emitted is proportional to
  light intensity
• Maximum kinetic energy of photoelectrons is
  proportional to the frequency and is independent
  of the intensity
• Electrons are emitted instantaneously, even at
  low intensities
• Classical physics could not explain the
  photoelectric effect but Einstein could!

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Einsteins Explanation

• EM waves are quantized
• Think of light as a stream of particles, called
  photons
• Photon energy given by Plancks equation
• When photons collide with electrons in metal,
  they transfer energy to electrons

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Einsteins Explanation

• If photon energy is greater than work function of
  the metal, photoelectrons are ejected
• If photon has more energy than the work function,
  the difference is the kinetic energy of the
  photoelectrons ejected from the surface

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Maximum KE of Photoelectrons
20
Compton Shift

• American physicist Arthur Compton (1892-1962)
  proposed that momentum energy should be
  conserved in a collision between photons
  electrons
• After a collision, scattered photon should have a
  lower energy, therefore a lower frequency (longer
  wavelength)
• In 1923, conducted experiments with X rays to
  demonstrate this change in wavelength, known as
  Compton shift.

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Models of the Atom

• Thomson Model / Plum Pudding Model
• Discovery of electron in 1897
• Negative electrons in sphere of positive charge

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Models of the Atom

• Rutherford Model / Planetary Model
• 1911 experiment by Geiger Marsden demonstrated
  that practically all of atoms mass and all
  positive charge must be centrally located in atom
  (nucleus)
• Electrons orbit nucleus like planets around Sun

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Problems with theRutherford Model

• Electrons orbiting the nucleus would undergo
  centripetal acceleration
• Accelerating electrons would radiate EM waves
• Electrons radiating EM waves would lose energy
• Loss of energy would cause electrons orbital
  radius to drop
• Frequency of emitted radiation would increase
• Electrons would rapidly collapse into nucleus
• Need a better model!

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Atomic Spectra

• Fill a glass tube with pure atomic gas
• Apply a high voltage between electrodes
• Current flows through gas tube glows
• Color depends on type of gas
• Light emitted is composed of only certain
  wavelengths

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Atomic Spectra

• Emission Spectrum diagram or graph that
  indicates the wavelengths of radiant energy that
  a substance emits (bright lines)
• Absorption Spectrum same thing, just for light
  absorbed by a substance (dark lines)
• What does this have to do with atomic models?

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The Bohr Model

• Similar to Rutherfords model, but only allows
  certain, discrete orbits
• Electrons are never found between orbits, but can
  jump from one orbit to another
• Electrons only emit radiation when they jump from
  an outer orbit to an inner one
• Energy of emitted photon is equal to energy
  decrease of electron. This determines frequency
  of emitted radiation.
• Energy of emitted photon is quantized only
  certain quantities are allowed. Hence, electrons
  undergo quantum leaps. (Obligatory pop culture
  reference)

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Energy Levels Emission Spectra

• Lowest energy state ground state
• Radius of this state Bohr radius
• Electrons usually here at ordinary temps
• How do electrons jump between states?
• Absorb photon with energy (hf) exactly equal to
  energy difference between ground state excited
  state
• Absorbed photons account for dark lines in
  absorption spectrum

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Energy Levels Emission Spectra

• Spontaneous emission
• Electron in excited state jumps back to a lower
  energy level by emitting a photon
• Does NOT need to jump all the way back to the
  ground state
• Emitted photon has energy equal to energy
  difference between levels
• Accounts for bright lines on emission spectrum
• Jumps between different energy levels correspond
  to various spectral lines

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The Bohr Model

• Successes

• Failures

• Account for wavelengths of all spectral lines of
  hydrogen
• Provides explanation for auroras
• Gave expression for radius of hydrogen atom
• Predicted energy levels of hydrogen
• Also successful when applied to hydrogen-like
  atoms (only one electron)

• Unsuccessful when applied to multi-electron atoms
• Did not explain why electrons do not radiate
  energy when in a stable orbit
• Did not explain why other orbits do not occur
• Combined classical and non-classical physics

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The Dual Nature of Light

• Is light a particle or a wave?
• Particle blackbody radiation, photoelectric
  effect
• Wave interference, diffraction
• Which model is correct?
• Both are correct, but depends on the situation
• Each phenomenon exhibits only one or the other
  natures of light
• True nature of light is not describable in terms
  of a single classical idea

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The Dual Nature of Light

• Low Frequency Light
• (Wave Nature)

• High Frequency Light
• (Photon Nature)

• Very low energy
• Difficult to detect a single photon
• Photon nature of light not evident
• Long wavelength
• Wave effects, like diffraction and interference
  are easy to observe

• Very high energy
• Easy to detect single photons
• Photon nature of light is evident
• Short wavelength
• Wave effects, like diffraction and interference
  are more difficult to observe

32
Matter Waves

• Since light can be described as either a particle
  or a wave, can we do the same for all objects,
  like atoms and people and cars?
• Louis de Broglie thought so!
• In 1924, proposed that all matter may have wave
  properties and particle properties
• Matter has a dual nature, just like light!
• Proposed idea of matter waves

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Matter Waves

• The larger the momentum of an object, the smaller
  its wavelength

34
Matter Waves

• Frequency of matter waves can be found with
  Plancks equation

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Evidence for Matter Waves

• 1927 Davisson Germer, showed that electrons
  can be diffracted by a single crystal of nickel
• Electron diffraction is possible because the de
  Broglie wavelength of an electron is approx.
  equal to distance between atoms (the size of the
  diffraction grating)
• Large-scale objects dont demonstrate this well
  because large momentum generates wavelengths much
  smaller than any possible aperture through which
  the object could pass (wont be diffracted)

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Bohr Model Explained

• De Broglie hypothesized that only certain
  electron orbits are stable
• Circumference of orbit must contain an integral
  multiple of electron wavelengths
• Similar to standing waves on a string

37
The Uncertainty Principle

• Wave nature of particles restricts the precision
  of our measurements
• Werner Heisenberg (1927)
• It is fundamentally impossible to make
  simultaneous measurements of a particles
  position and momentum with infinite accuracy
• The more we learn about a particles momentum,
  the less we know of its position, and vice versa.

38
The Uncertainty PrincipleA Thought Experiment

• Imagine trying to measure an electrons position
  and momentum with a powerful microscope
• In order to see the electron, thereby determining
  its location, at least one photon of light must
  bounce off the electron and pass through the
  microscope to your eye
• When the photon strikes the electron, it
  transfers some energy momentum to the electron.
  So we are less sure of the electrons momentum.

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The Uncertainty PrincipleA Thought Experiment
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Schrodingers Wave Equation

• Erwin Schrodinger (1926) proposed a wave equation
  for de Broglies matter waves
• Each particle can be represented by a wave
  function , ?, dependent on the position of the
  particle and time

41
The Electron Cloud

• Max Born (1926) interpreted Schrodingers wave
  function to show probability of finding an
  electron at certain locations
• ?2 is proportional to probability of finding
  the electron at a certain position
• Peak probability for an electron in the ground
  state corresponds to Bohr radius

42
Quantum Mechanical Model

• Electrons are not confined to particular orbital
  distances as assumed in Bohr model
• Electron cloud a probability cloud
• Density at each location related to probability
  of finding electron at that location
• Wave function predicts geometry for energy levels
  (some spherical, others more complex)
• Most probable location still corresponds to Bohr
  radii, but impossible to determine actual
  location
• Mathematical picture of the atom that explains
  certain aspects of atomic structure that Bohr
  model cannot explain