Quantum Mechanics the world is weird

Rutherford’s Experiment most Source: Griffith

Atomic Emission Spectra Source: Griffith Emission Spectrum of Hydrogen Why not continuous? More spectra at http://javalab.uoregon.edu/dcaley/elements/Elements.html

Bohr Model Only certain energy levels are allowed Emits light only when electron changes energy level Source: Griffith

Bohr’s model Fits H perfectly Also works for “H-like” ions Strictly wrong, but important in development of QM Helps us to see how QM ideas evolve

Bohr’s Postulate Electron angular momentum is quantized L = nh h = h/2p pronounced “h bar”

de Broglie’s Wild Idea Maybe electrons act as waves! Standing waves can have only specific wavelengths—could something like this explain line spectra?

de Broglie’s Wild Idea Can electrons act as waves? Light can act as a particle. Momentum of a photon: p = h/l p = momentum h = Planck constant = 6.626  10-34 J s l = wavelength

de Broglie’s Wild Idea What is an electron’s wavelength? p = h/l solve for l l = h/p

Electrons: de Broglie and Bohr nl = 2pr nh/p = 2pr nh/(2p) = rp This is the Bohr condition that angular momentum is quantized in increments of h/(2p).

Explains Bohr’s Quantization standing waves nl = 2pr Source: Griffith

Waves and Uncertainty Energy known exactly, position not determined Energy less specific, position more specific Energy not determined, position known exactly

Heisenberg Uncertainty Principle Dp Dx  h/2 Dp = uncertainty in momentum Dx = uncertainty in position h = h/2p = 1.05459  10-34 J s

Question The uncertainty principle tells us that A. Particles have wave-like properties. B. You cannot specify both position and momentum beyond a certain accuracy. C. Quantum physics is really wild. D. All of these.

Electron Energy Levels The electrons do not collapse onto the proton because: Smaller radius  smaller Dx, l This requires higher f, Dp  higher energy!

Circular membrane standing waves Describing Electrons Electrons are standing waves! Circular membrane standing waves edge node only diameter node circular node Source: Dan Russel’s page Higher energy  more nodes

Experimental Verification Electrons and neutrons diffract. Diffraction patterns match l = h/p.

Waves and Quantization Boundary conditions allow only certain wavelengths to be sustained

Born Interpretation What is a matter wave? Square of amplitude |Y|2 is probability density if Y is normalized to |Y|2dV = 1 Probability of being in region dV is ∫|Y|2dV Still detected as particles

What is Y? “Wave function” Everything we “know” about a particle Function of space and time Y(r,t)

Electron Orbitals Electrons’ position and energy described as standing waves! Higher energy  more nodes Exact shapes given by four quantum numbers No two electrons can have the same four quantum numbers

Hydrogen Orbitals Source: Chem Connections “What’s in a Star?” chemistry.beloit.edu/Stars/pages/orbitals.html

Chemistry in Five Minutes Molecules Chemistry in Five Minutes

Covalent Bonding Electrons shared more space Electrons not shared lower energy longer wavelength

Dipole-Dipole Forces Some molecules have permanent dipoles… + - …and attract each other like bar magnets! + -

Charge-Fluctuation Forces All molecules have fluctuating dipoles… …and attract each other when their electrons move in synchrony.

Summary Atoms comprise massive, positively-charged nuclei surrounded by light, negatively-charged electrons. The uncertainty principle prevents atoms and molecules from collapsing. Atomic and molecular behavior is described by wavefunctions.

Summary Electrons in atoms can have only specific energies. Chemistry is governed by electrical forces and quantum uncertainty.