Models of the Atom

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 - 1890’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 = 10-15 m Size of atom = 10-10 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

A high school teacher named Balmer found that these wavelengths obeyed a 1/n2 rule Shows visible portion of spectrum Divide by 10 to get nanometers

Infra-red Visible Shows Energy of emitted photons UV

One Formula Fits All(but no one knew why it worked) • Each observed wavelengthdescribed by • 1/l = R (1/n’2 – 1/n2) n’ = 1 for Lyman, n’ = 2 for Balmer, n’ = 3 forPaschen R = Rydberg Constant = 1.097 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 = Eu - El Eu hf El

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

Bohr Theory for Hydrogen Atom • Electron and Nucleus held together by Coulomb force • Predicts r1 =0.529 x 10-10 mas radius of smallest oribit in hydrogen (Bohr Radius) • Leads to Lyman, Balmer, Paschen formulae • En = -13.6 eV/n2 • Ground state has most negative energy • Excited states have higher(more positive) energy

Bohr’s Derivation • F = ma • kZe2/ (rn) 2 = mv2 /rn • Mvrn =nh/2p • rn = n2h2/(4p2mkZe2) • En= ½ mv2 – kZe2/rn = -2p2Z2e4mk2/n2h2 • En = - 13.6/n2

Bohr Radii • Ground state has smallest radius • Excited states have larger radii • r = n2 r1 • Changes in level are called atomic transitions

Bohr Energy Levels for Hydrogen Atom

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

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 = E2 – E1 = 13.6 eV – 3.40 eV = 10.2 eV l = c/f = hc/(E2 – E1) = (6.63x10-34 J-S)(3.00x108 m/s)/(10.2 eV)(1.6 x 10-19 J/eV) = = 1.22 x 10-7 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 l = h/mv • Only orbits that correspond to standing waves can persist • Circumference must contain whole number of wavelengths

Standing Circular Waves • 2prn = nl n = 1, 2, 3 But l = h/mv 2prn = nh/mv or mvrn = nh/2p Thiswas 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)

Models of the Atom