Models of the Atom Rutherford, Bohr, De Broglie and Quantum Physics

Nature of Electrons Originally called cathode rays Reversing magnet shows that they are charged particles

Plum Pudding Model (Thompson ’s) Positively charged material

Rutherford Experiment (1911) Alpha Particle is 2n2p or helium nucleus

Another View

Results of Rutherford Experiment Most alpha particles pass through undeflected Conclusion: atom is mostly empty space Some deflected at very large angles, even backward Conclusion:positive charge is concentrated in a small region of atom Animation

Rutherford’s Planetary Model of Hydrogen Atom Size of nucleus = m Size of atom = m

Two problems Stability Continuous spectrum not seen

Atomic Spectra Observe with gas discharge tube Glow due to accelerated electrons striking atoms in low pressure gas and exciting them Light from tube found to contain discrete wavelengths

Spectrometer Set Up

Emission Spectrum Use diffraction grating or prism spectrometer to see Compare to white light spectrum(continuous) Graphics courtesy of Science Joy Wagon Physics Zone

Shows visible portion of spectrum Divide by 10 to get nanometers A high school teacher named Balmer found that these wavelengths obeyed a 1/n 2 rule

Visible UV Infra-red Shows Energy of emitted photons

One Formula Fits All (but no one knew why it worked) Each observed wavelength described by 1/  R (1/n’ 2 – 1/n 2 ) n’ = 1 for Lyman, n’ = 2 for Balmer, n’ = 3 for  Paschen R = Rydberg Constant = x 10^7 m^-1

Rutherford Model Could Not Explain… Why atoms emit line spectra Why atom is stable. Accelerated electrons should emit radiation with increasing frequency as they spiral into atom. Spectra should be continuous.

Bohr Model Atom has discrete energy levels - states Electrons move in orbits without radiating energy Light quanta (photons) emitted when electrons jump from state to state hf = E u - E l EuEu ElEl hf

Bohr – Balmer Connection Bohr’s theory agrees with Balmer if electron angular momentum quantized L = mvr n = n h/2  n = 1, 2, 3, … r n is radius of nth possible orbit

Bohr Theory for Hydrogen Atom Electron and Nucleus held together by Coulomb force Predicts r 1 = x m as radius of smallest oribit in hydrogen (Bohr Radius) Leads to Lyman, Balmer, Paschen formulae E n = eV/n 2 Ground state has most negative energy Excited states have higher(more positive) energy

Bohr’s Derivation F = ma kZe 2 / (r n ) 2 = mv 2 /r n Mvr n =nh/2  r n = n 2 h 2 /(4   mkZe 2  E n = ½ mv 2 – kZe 2 /r n = -2   Z 2 e 4 mk 2 /n 2 h 2 E n = /n 2

Bohr Radii Ground state has smallest radius Excited states have larger radii r = n 2 r 1 Changes in level are called atomic transitions

Bohr Energy Levels for Hydrogen Atom n E n = eV/n eV eV eV eV

Ionized atom, positive continuous energies, electron free E = 0 E = -3.4 eV E= -1.5 eV Ground state E=-13.6 eV

Emission vs. Absorption of Photon Energy Emission- atom drops to lower states Random and spontaneous process Absorption – atom rises to higher states. Only photons of just the right energy can be absorbed

Question: If you shine a light on a gas do you get Absorption? Emission? Both?

Ionization Energy Minimum energy to kick electron out of ground state 13.6 eV for hydrogen atom Can supplied by heating or collision

Find the Wavelength What is the wavelength in the transition from n=2 to n=1? hf = E 2 – E 1 = 13.6 eV – 3.40 eV = 10.2 eV = c/f = hc/(E 2 – E 1 ) = (6.63x J-S)(3.00x10 8 m/s)/(10.2 eV)(1.6 x J/eV) = = 1.22 x m or 122 nm What kind of light is this?Ans. Ultra Violet

De Broglie Waves in Atoms Why should orbits be quantized a la Bohr? De Broglie; wave is associated with electron  = h/mv Only orbits that correspond to standing waves can persist Circumference must contain whole number of wavelengths

Standing Circular Waves 2  r n = n  But  = h/mv 2  r n = nh/mv or mvr n = nh/2  This  was Bohr’s quantization condition Implies wave-particle duality at root of atomic structure 

Limitations of Bohr Theory Could not explain spectra of other than hydrogen atoms Could not explain why emission lines are double, triple or more Could not explain why some lines brighter than others Could not explain how atoms bond Mixed classical and quantum ideas

Quantum Mechanics Next step after Bohr in explaining atomic physics Explains details of spectra Gives classical(correct) results for larger objects Based on “Wave functions,” probability and Schrodinger equation Modern theory called “quantum electrodynamics.”

Heisenberg Uncertainty Principle Accuracy of some measurements is inherently limited by nature To observe is to interfere We cannot measure the momentum and position of an object precisely at the same time The energy of an object may be uncertain(or even non-conserved) for a small time

Probability vs Determinism On sub-atomic scale nature is probabilistic not deterministic Certain paths and events knowable only in terms of probability Electrons form cloud around atom called probability distribution

Quantum Numbers Determine State of Atom Principle quantum number-from Bohr theory Orbital quantum number-related to angular momentum Magnetic quantum number-related to direction of electron’s angular momentum Spin quantum number

Pauli Exclusion Principle No two electrons in an atom can occupy the same state Can’t have exactly the same quantum numbers Helps determine patterns of regularities in Periodic Table of Elements(explained by quantum mechanics)