The Atom and the Quantum

The Atom and the Quantum

1. Corpuscular Theory

   • Robert Boyle propose theory as alternative to the atomic theory. States that corpuscules were divisible particles that could change the characteristics of other matter. Issac Newton advocate the corpuscular light theory in Optiks.

2. Antoine Lavoisier

   • French chemist documented the first canonical list of elements that formed the basis of the periodic table.  He identified and named H and O by studying combustion in isolation.  He discovered the Law of Conservation of Mass. 
   • Joseph Proust
     • He determined that elements could only combine with one another in certain fixed proportions. 

3. Dalton's atomic theory

   • Dalton discovered that during chemical reactions, elements were used up only in specific ratios of whole numbers by weight.  Dalton created the first atomic theory: Elements are made of atoms             Atoms of the same element are identical to one another             Atoms cannot be created, destroyed, or divided             Atoms combine in simple ratios to form chemical compounds              Atoms recombine during chemical reactions
   • Periodic Table

4. Thomson's Plum Pudding Model

   • J.J. Thomson measured the mass of a cathode ray particle and it was 1800 times smaller than the lightest know atom (hydrogen).  Later named the particles electrons.  First to put forward idea that they were a part of the atom.  Model consists of positively charged sphere with electrons scattered throughout.  
   • Cathode Ray
     • Michael Faraday discovered that when an electric voltage was placed across glass tubes of evacuated air, positively charged end glows.  an invisible beam passes from cathode to anode.  Before plasma screen and LCD, tvs and computers used cathode rays 

5. Rutherford's Planetary Model

   • Ernest Rutherford directed a beam of positively charged particles at gold foil to measure the angle at which the particles deflected (gold foil experiment) Discovered the nucleus that must be positively charged. Electrons orbit around the nucleus.  Did not explain two important phenomena:        Thermally excited atoms had been observed that only specific frequencies of electromagnetic radiation          Classical physics held that when charged particles accelerate, they emit electromagnetic waves. If electrons orbited around the nucleus, they would spiral into the nucleus and implode. 

6. The Wave Theory of Light

   • Christian Huygens envision light as a wave propagating radially outward from the source. Explains how light diffracts around around corners and through apertures. 
   • Double Slit interference
     • Thomas Young discovered the phenomena where light passing through two thin parallel slits produces a pattern of bright and dark fringes on  a screen. (Due to constructive and destructive interference)
   • James Clerk Maxwell
     • Theory of electromagnetism: light was a wave of oscillating electric and magnetic fields propagating through space.
   • Electromagnetic spectrum
     • Entire range of possible electromagnetic waves. All electromagnetic waves travel at the same speed and differ in frequency.  Waves with long wavelenghts hav low frequencies and waves with short wavelengthshave high frequencies.

7. Energy Quantization

   • All matter that has a temperature above 0k radiates thermal radiation. At room temperature, intensity of radiation is so low we do not perceive it.  Thermal radiation is emitted as a continuous range of wavelengths. 
   • Blackbody
     • An idealized object that absorbs all radiation that it encounters and emits electromagnetic waves to remain in thermal equilibrium. 
   • Ultraviolet Catastrophe
     • For radiation with long wavelengths, classical theory held, but the contrary for radiation with short wavelengths. Classical theory predicted the intensity of radiation as the wavelength approached zero, yet ultraviolet is on the short wavelength side of the visible light spectrum. 
   • Plank's Constant
     • Plank proposed that the energy of an oscillating atom could only take certain discrete values that are multiples of a quantum number. The constant resolved the ultraviolet catastrophe.   E= nhfh= 6.63x10^-34 Energy is quantized.
   • Photons
     • Photoelectric Effect: Henrich Hertz discovered that metals with ultraviolet light produced sparks. The sparks were actually electrons being ejected from the surface.  
     • Lenard's Experiments
       • 1. Electrons were emitted instantly after the metal was illuminated. 2. Light below a certain frequency did not eject electrons, regardless of light intensity. 3. Increasing the light intensity did not cause electrons to be ejected with greater kinetic energy. 4. Increasing the light frequency resulted in higher- energy electrons being emitted.
     • Albert Einstein
       • Propose light is quantized.  Photoelectric effect can only be explained as a quanta of light colliding with electrons, transferring energy and ejecting the electrons.  Photon= Light quanta 
     • Compton Scattering
       • Compton observed X- ray radiation colliding with and scattering off of free electrons, thereby losing energy and shifting frequency.  Cannot be explained by purely wave view light. 
   • Atomic Spectra and the Rydberg Formula
     • Atoms emit characteristic frequencies of light, called atomic spectra, when excited.  Atomic spectra help identify which atoms are present in a sample. 
     • Emission spectrum
       • A set of wavelengths emitted by excited atoms that can be viewed with a spectroscope. 
     • Absorption spectrum
       • Created by passing white through a collection of atoms.  Occurs at same wavelength as emission spectrum. 
     • atomic spectroscopy
       • The process of analyzing spectral lines to identify the chemical makeup of a sample.  Solar atomic spectroscopy discovered helium. 
     • Rydberg formula
       • Balmer discovered the relationship between the wavelengths present in the visible hydrogen emission spectra.  Rydberg generalized Balmer's expression. 1/(wavelength)= R(1/m -1/n^2)

8. Bohr Model of Hydrogen

   • Assumptions: 1. Electrons revolve about the nucleus in circular in circular orbits. 2. Electrons can only occupy certain energy levels. They do not radiate energy as a result of their circular motion.  3. Electrons can move to higher energy levels by absorbing electromagnetic radiation. Vise Versa. 
   • Model
     • Modified Rutherford's planetary model.  Key modification in the fact that electron angular momentum could only occur in integer multiples of h/ 2pi
   • Energy levels
     • energy levels of the hydrogen atom indexed by quantum number n= 1.2.3... Lowest allowable energy state is known as ground state (n=1). r= n^2a Calculates Bohr radius.  
     • energy states and ionization energy
       • Excited States: energy states higher than ground state Ionization energy: amount of energy required to excite an electron to the point that it removes. 
     • Balmer series
       • Set of emission lines on the visible spectrum resulting from a hydrogen atom transitioning to a higher energy level. 
     • Correspondence Principle
       • As quantum number increases, difference in energy between successive hydrogen levels becomes smaller.  Agrees with classical predictions. 
   • Electron Volt
     • The energy of a single electron accelerated by an electric potential difference of 1 volt. E= -(13.6eV0/n^2 Negative sign indicates the electron does not have enough energy to escape from atom (electron is bound the nucleus)
   • Model Limitations
     • Helium cannot be accurately modeled.  Certain spectral lines appear to be to be made in the fashion of structure splitting and the model could not account for the effects. Could not explain how atoms combined to form molecules. 

9. The De Broglie Hypothesis

   • First to propose the matter could be treated as having wave- like characteristics in the same way that light could be treated as having particle- like characteristics.  (Wavelength)= h/p Provided a retroactive justification for Bohr's assumption that the electron's angular momentum is quantized. 
   • Clinton Davisson and Lester Germer
     • Directed beam of electrons at a crystalline nickel target.  Noticed that electrons exhibiting same diffraction pattern.   Prove wave nature of elections.
   • Wave nature of matter
     • Transmission electron microscope relies on wave properties to achieve a greater resolving power. 

10. Wave- Particle Duality

    • Light and matter exhibit properties of both waves and particles, depending on experiment.  Double slit interference raises question: did the photon travel through one slit or both or neither? With quantum theory, there is "no" photon until detection occurs.  Its impossible to predict location of an individual photon detection.

11. Modern Quantum Mechanics

    • Emerged to provide more complete and consistent description of physics at scales where quantum effects are dominant. 
    • Wave Functions and the Schrodinger
      • Described the behavior of deBroglie's "matter waves"
      • Wave functions
        • Solutions to the Schrodinger equation.  Max Born propose that absolute square of wave function equaled the particle's probability density of being detected.  At the quantum scale, a particle constrained to a small space can only occupy certain fixed energy levels. 
      • Quantum tunneling
        • The probability of tunneling is dependent on the width of barrier and energy of the wave.  Scanning Tunneling Microscope can map out the surface with resolution sufficient enough to distinguish individual atoms. 
      • Newtonian Mechanics
        • Newtonian Mechanics: objects can be described as having a position and velocity that are well defined at any instant. Newton's Laws predict the path and where it will be at any future moment. (this view of natural world called "deterministic")
      • Quantum mechanics and probability
        • Quantum mechanics describes the submicroscopic world as being "probabilistic". Cannot predict the result of a quantum measurement.  SCHRODINGER'S CAT
      • Heisenberg Uncertainty Principle
        • The measurement of any quantity requires level of uncertainty (limitations of instrument precision and environmental effects). Why laboratory procedures must be repeated multiple times to obtain average value.  On the quantum scale, measurements are altered by the act of measuring them.  (*triangle*x)(*triangle*p)>h/2pi We cannot simultaneously measure both the position or momentum with full precision. 
        • Mr. Tompkins in Wonderland
          • A bank teller explores a "quantum jungle" where Plank's constant id larger than normal value. As a result, elephant appears "fuzzy" due to uncertainty of position.
    • Modern Quantum Model
      • Amplitude of the wave function at a given point in space yields probability of detecting an electron. Nucleus is surrounded by an "electron cloud" with regions where an electron may be detected with varying probability. 
      • Orbitals
        • Orbital quantum number L can take non- negative integers values 0 to n-. Electrons with the same value for L and n occupy the same subshell (s, p, d, f)
      • Zeeman effect
        • The effect causes individual spectral lines to separate into multiple distinct lines of similar frequency. 
      • Spin
        • Quantum # m result from experiments.  Electrons belong to fermions who have a 1/2 integer spin.  The spin quantum number is NOT connected the spin about its axis. 
        • Magnetic moment
          • Electron has an intrinsic magnetic moment.  Measure of an object's tendency to align with a magnetic field. Atoms with filled shells have no magnetic moment (diamagneitc). Atoms with partially filled shells and an uneven number of electrons have an overall magnetic moment (paramagnetic).  Ferromagnetic= atoms with uneven number of electrons that tend to align even with no magnetic field. 
      • Pauli exclusion principle
        • No two electrons can have the same values for the quantum numbers in n, L,m.  The stacking property in electrons help explain the chemical properties. (Noble Gases)
        • Bosons
          • Has an integer spin an are NOT subject to the Pauli Exclusion so they can occupy the same state. 
        • Bose- Einstein condensate
          • If gas of bosons were cooled close to absolute 0, they would collectively fall to the lowest energy state. 

12. Applications of Atomic Physics

    • Lasers
      • Atom can become excited from a lower to higher energy state by absorbing a photon.  The atom will return to a lower state through "spontaneous emission" of a photon or "stimulated emission". A continuated chain reaction og stimulated emission in a focused beam of 1 wavelength, coherent light. 
      • Acronym
        • Light  Amplification by Stimulated  Emission of  Radiation
      • Characteristics
        • Monochromatic: because emitted photons all correspond to the same energy transition, they all have exactly the same frequency. Directional Coherent: the light waves are "inphase" (peaks and troughs align)
      • Principles
        • Must be metastable (last long before returning to ground state).  Must be prepared so that more are in an excited state than are in ground state (population inversion).
      • Laser cooling
        • Lasers can be used to control and slow down the collection of atoms so their behavior is determined only by quantum mechanics. 
    • Doppler effect
      • The apparent frequency of a wave is shifted due to relative motion between the source and the receiver.