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Wave Nature of Light • Rutherford’s model of the atom could not explain chemical behavior • Bohr and others described the arrangement of electrons around the nucleus • These arrangements could account for differences between the elements • Bohr’s model was based on spectroscopic evidence Electromagnetic Radiation • Light can be described as though it is a wave Parts of a wave • Amplitude and wavelength Crest Trough Wave Stuff • Amplitude: Vertical distance from crest to midline (meters) (brightness/intensity) • Wavelength: Horizontal distance from crest to crest (meters) (color) • Velocity: Rate at which wave travels (3.00x108 m/s in a vacuum) (constant) • Frequency: # waves that pass a given point per unit time (waves/sec, cps, hertz, s-1) High frequency Low frequency Wave Math • Velocity = wavelength x frequency • Velocity = c Wavelength = l Frequency = n • c = ln • Since c is constant, l and n are inversely related Example problems • Find the frequency of purple light (wavelength 455 nm). • Solution: c = ln, or n = c/l Wavelength must be in meters, since c is in m/s: 455 nm = 4.55x10-7 m n = (3.00x108 m/s)/(4.55x10-7 m) = 6.59x1014s-1 Example #2 • Find the wavelength of violet light with a frequency of 4.56x1014s-1. • c = ln or l = c/n • l = (3.00x108 m/s)/(4.56x1014s-1) = 6.58x10-7m (658 nm) Particle Nature of Light • Light also acts as a particle: proposed by Newton • Max Planck and glowing blackbodies: energy is quantized • Smallest energy unit available is a quantum • Energy of quanta depends on the frequency of the energy: E = hn Particle Nature of Light • h is Planck’s constant: 6.626x10-34Js • Energy is directly proportional to frequency • Energy is inversely proportional to wavelength: E = hn and n = c/l so E = hc/l Light Particle Sample Problem • Find the energy of a microwave photon having a wavelength of 3.42x10-2m. • Solution: E = hc/l = (6.626x10-34Js)(3.00x108m/s)/3.42x10-2m = 5.81x10-24J Photoelectric Effect • Certain metals will eject electrons when exposed to light • Number of electrons ejected depends only on the intensity of light • No electrons ejected by light below certain frequency Photoelectric Effect • Could not be explained by wave model of light • Einstein explained effect using quantum theory of light • He won the Nobel Prize for his work (not for relativity) Atomic Emission Spectra • When elements are zapped with energy, they give off light • Light is first shone through a slit • When light is shone through a prism, colors are separated • Only some of the colors appear as fine lines against a dark background Emission spectra of common fluorescent bulbs Emission Spectrum Setup Absorption Spectra • In absorption spectra, light is shone through cold gas or liquid • Light then goes through a slit and prism or grating • Resulting spectrum is continuous except for dark lines Absorption Spectrum Absorption Spectrum of Chlorophyll Liquids tend to have less distinct absorption spectra Gas Absorption Spectra Absorption Spectrum Setup Spectra Types Bohr Model of the Atom • Bohr wanted to explain the presence of sharp lines in the hydrogen spectrum • He proposed that hydrogen’s electron could only have certain distinct energies • These energies were integral multiples of some minimum energy • The energy levels correspond to differently sized orbits Bohr’s Atom • Spectral lines were due to electrons jumping from one level to another. • Incoming energy promotes an electron to a higher energy level • When the electron returns to the lower level it releases energy Quantum Numbers • Bohr assigned the energy levels numbers • The Principle Quantum Number (n) represents the main energy level • n can only have non-zero integral values • n = 1, 2, 3, ... Why quantum numbers? • • • • Louis de Broglie: Wave-particle duality As a wave: E = hc/l As a particle: E = mc 2 Combined: hc/l = mc 2 l = hc/mc 2 = h/mc • For objects moving slower than light, replace c with v (velocity): l = h/mv Particle wavelength problems • Every particle has a wavelength • The larger the particle, the shorter the wavelength • Example: Calculate the wavelength of an electron moving at 0.80c (mass = 9.109×10-31 kilograms). • Solution: l = h/mv = 6.626x10-34Js/[(9.109×10-31kg)(0.80)(3.00x108m/s)] = 3.0x10-12m (smaller than an atom, bigger than a nucleus) Particle wavelength problems • Find the wavelength of a baseball (145g) thrown toward home plate at 95.0 mph (42.5 m/s) • Solution: l = h/mv = 6.626x10-34Js/[(0.145kg)(42.5m/s)] = 1.08x10-34m (much smaller than a nucleus) Back to quantum numbers • Only certain orbits are allowed because they are the only ones in which an integral number of wavelengths can “fit”. • “In-between” orbitals would require a fractional number of wavelengths. “I think it is safe to say that no one understands quantum mechanics.” Physicist Richard P. Feynman Heisenberg Uncertainty Principle • It is impossible to know both the position and momentum of an electron simultaneously • The only way to know anything about an electron is to shoot it with a photon • The photon alters the position and/or momentum in an unpredictable manner, so the original position and momentum remain unknown. More Energy Levels • The fine lines in emission spectra are actually made up of several even finer lines • Each energy level has sublevels • Each sublevel has a shape • Each sublevel has one or more orbitals • Each orbital holds two electrons • How do we sort all this out? Using Quantum Numbers! • Four quantum numbers are needed in Schrödinger’s equation to describe the probability function of an electron • n = principle quantum number = 1, 2, 3, ... Main energy level – determines size of orbital • l = azimuthal quantum number = 0, 1, ... n-1 Sublevel – determines orbital shape Well-used quantum numbers • s: p: d: f: • m l = 0 (first two columns of PT) l = 1 (last six columns of PT) l = 2 (middle ten columns of PT) l = 3 (bottom two rows of PT) = magnetic quantum number = - l to +l Specifies orbital – determines orientation • s = spin quantum number = ±½ Specifies spin Orbital shapes • s orbital: spherical • Every energy level has an s orbital: 1s, 2s, etc. • Higher level s orbitals are lobed • Nodes are areas of minimum electron density • One node is added for each level • s sublevel: one orbital, two electrons p orbital • p orbitals are dumbbell shaped • p sublevel (l = 1) consists of three orbitals: px py pz (six electrons) • Three p orbitals are orthogonal to each other • Only present after first main energy level (n>1) d orbital • d orbital is cloverleafshaped • Five orbitals, ten electrons make up d sublevel • Only available when n>2 f orbitals • Complicated shape • Seven orbitals, fourteen electrons • Only available when n>3 Allowed quantum number combinations • Pauli exclusion principle: no two electrons can have the same set of four quantum numbers • Aufbau principle: electrons fill the lowest energy state available first • Lower numbers mean lower energy (n and l) • Various m and s states are degenerate (of equal energy) Allowed Quantum Number Combinations n l 1 0 1 0 1s sublevel – m 0 0 2e- s +½ -½ 2 0 0 2 0 0 2s sublevel – 2e- +½ -½ n l 2 1 2 1 2 1 2 1 2 1 2 1 2p sublevel – m -1 -1 0 0 1 1 6e- s +½ -½ +½ -½ +½ -½ Allowed Quantum Number Combinations 3s and 3p are and 2p 3d sublevel: n l 3 2 3 2 3 2 3 2 similar to 2s m -2 -2 -1 -1 s +½ -½ +½ -½ n l 3 2 3 2 3 2 3 2 3 2 3 2 3d sublevel - m 0 0 1 1 2 2 10e- s +½ -½ +½ -½ +½ -½ Electron configurations • Electron configurations show the location of every electron in the atom • Electrons follow three rules: Pauli exclusion principle, Aufbau principle, Hund’s rule • Each orbital is represented by a box and a symbol, and each electron by an arrow. Electron configurations More Electron Configurations Hund’s rule: When putting electrons into degenerate orbitals, do not pair them until necessary. More Electron Configurations More Electron Configurations Orbital filling diagrams Orbital filling diagrams Noble Gas Shorthand Structures • Noble gas symbols can be used to represent the core electron structure • Manganese (25 e-): 1s2 2s2 2p6 3s2 3p6 4s2 3d5 • Equivalent to [Ar] 4s2 3d5 Electron Dot Structures • Electron dot structures represent only the valence electrons • Valence electrons are the electrons in the outermost energy level (highest value of n) • The maximum number of electrons allowed in the valence shell is 8 Electron dot structures • Consists of the element’s symbol and dots representing the valence electrons Hydrogen: H Helium: He Lithium: Beryllium: Sodium: Be Na Nitrogen: Iron: N Fe Li Neon: Ne Lead: Pb