* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Figure 7.18 The 3d orbitals
Renormalization group wikipedia , lookup
Bremsstrahlung wikipedia , lookup
Hidden variable theory wikipedia , lookup
Double-slit experiment wikipedia , lookup
Renormalization wikipedia , lookup
Planck's law wikipedia , lookup
Particle in a box wikipedia , lookup
X-ray photoelectron spectroscopy wikipedia , lookup
Quantum electrodynamics wikipedia , lookup
Molecular orbital wikipedia , lookup
Ultraviolet–visible spectroscopy wikipedia , lookup
Electron scattering wikipedia , lookup
Magnetic circular dichroism wikipedia , lookup
Rutherford backscattering spectrometry wikipedia , lookup
Astronomical spectroscopy wikipedia , lookup
Bohr–Einstein debates wikipedia , lookup
Hydrogen atom wikipedia , lookup
Tight binding wikipedia , lookup
Atomic orbital wikipedia , lookup
Electron configuration wikipedia , lookup
Matter wave wikipedia , lookup
Theoretical and experimental justification for the Schrödinger equation wikipedia , lookup
Atomic theory wikipedia , lookup
Chapter 7: Quantum Theory and Atomic Structure E-M RADIATION: LIGHT Electro-Magnetic radiation includes visible light, microwave, TV, radio, x-ray, etc. Radiation is a combination of vibrating electric and magnetic fields in repeatable waveforms Wavelength, λ (lambda): distance from crest to crest Frequency, (nu): # crests to pass a point in 1 second, units are #/s or Hz Wave velocity = λ All E-M radiation in a vacuum has constant velocity called the speed of light: c = 2.998 x 108 m/s. Therefore c = λ (Memorize formula and c) Long λ => short & vice-versa Figure 7.1 Frequency and wavelength Figure 7.2 Amplitude of a wave Figure 7.3 Regions of the electromagnetic spectrum (Visible light is a very small portion.) Sample Problem 7.1a (you do the work here) Note A = Angstrom, an old unit of wavelength. Conversion is 1A = 1.0 x 10-10 m. E-M RADIATION E-M radiation was considered to be a wave/energy phenomenon and not matter Max Planck developed a new physics when classical physics could not be used to interpret data from blackbody radiation Blackbody radiation is emitted by solid bodies that are heated to high T and become incandescent Classical physics had to assume continuous radiation, and it could not resolve the data that there was discrete radiation Planck developed theory of Packets of Energy called quanta The energy associated with quanta was proportional to the frequency of the radiation: E = h h = Planck’s constant 6.626 x 10-34 J.s Wavelength, Frequency and Energy If c =, and E = h, then with rearranging and substituting: E = hc/ What is the energy of a photon with a wavelength of 399.0 nm? (from 4th ed. Figure 7.6 Blackbody radiation) Figure 7.6 Demonstration of the photoelectric effect Photoelectric Effect Photoelectric Effect: electrons are ejected from a metal's surface if it is exposed to uv radiation Each metal required a characteristic minimum uv frequency to start ejecting e-s Called Threshold freq, o - As increases more e-s ejected with higher vel (more KE) These data also defied classical physical explanation Einstein reviewed data, recalled Planck's quanta The "incident" radiation consists of quanta of energy, E = h, called photons - thus the PHOTOELECTRIC Effect In order to eject an e-, a min KE is required, E = ho If E>ho then excess KE is supplied to the e-, increasing its velocity Chapter 7: Quantum Theory and Atomic Structure For Na metal, o = 5.51 x 1014 Hz Sample Problem 7.2: (you do work here) Line Spectra Experiments with "excited" atoms of H produced emission spectra - always a discrete set of lines at certain wavelengths White light dispersed by a prism or diffraction grating: - we see ROYGBIV – a continuous spectrum from 750 nm to 400 nm When a gas-filled tube is charged with current, only certain EM 's are detected - called a line spectrum or emission spectrum The gas particles split into individual atoms The e-s are excited by the current into a higher energy level. When they drop down, they emit energy of a certain λ, with energy gaps at distinct intervals Figure 7.7 The line spectra of several elements (Compare the continuous spectrum of visible light vs. the discrete or line spectra of the three elements shown.) Line Spectra and Energy Levels Hydrogen atomic line spectra – also called emission spectra – - worked out mathematically (by several scientists) to define the energy of the light emitted & relationships between the lines Balmer: red, green & blue lines (656.3, 486.1, 434.0, 410.1 nm) 1/λ = Ry(1/22 - 1/n2) If n > 2 Ry = Rydberg constant = 1.096776 x 107/m If n = 3 get red, n = 4 get green, n = 5 get blue, n =6 get violet Figure 7.8 Three series of spectral lines of atomic hydrogen. Balmer is in the visible region and the other series, which have names also, are in uv or ir area of E-M radiation. The Bohr Model of Hydrogen atom 1. H atoms have only certain allowable energy levels called stationary states. 2. Atom does not radiate energy while in a stationary state. 3. Atoms changes to another stationary state by absorbing or emitting a photon. Energy=EstateA-EstateB=hn What line spectra mean Bohr found En = - Rhc/n2 where R = 1.097 x 107/m, h = 6.626 x 10-34 J.s, c = speed of light Rhc = 2.178 x 10-18 J (since they are all constants) Then En= -2.178 x 10-18 J/n2 All E is therefore < 0, and has discrete values only Nucleus (proton) & e- are so far apart there's no attraction anymore Negative E is more stable than zero energy n = 1 is the ground state, all above are excited states Figure 7.9 Quantum staircase Figure 7.10 The Bohr explanation of the three series of spectral lines Chapter 7: Quantum Theory and Atomic Structure Emission vs. Absorption Spectroscopy - Instrumental techniques used to obtain information about atomic or molecular energy levels - Emission: electrons in an atom are excited to a higher energy state and then emit photons as they return to lower energy states - Absorption: electrons in an atom absorb photons of certain wavelengths and jump to higher energy states; photons NOT absorbed are observed! - See Figure 7.11 in text: why chlorophyll looks green Figure B7.1 (4th ed.) Flame tests Practice sample problem 7.3 and its follow-up problem. A hydrogen atom has an e- excited up to level 4, and it drops back to level 2. (a) determine the wavelength of the photon emitted and (b) the energy difference. (a) Use 1/ = Ry(1/22 – 1/42) = 4.8617 x 10-7 m (b) Use E = hc/ E = 4.086 x 10-19 J Follow-up: Answer the same questions for the e- excited up to level 6. "Traveling waves" vs. stationary waves or standing waves Stationary wave: - fixed at both ends - has "nodes" - never moves on those spots with distance = length/2 Only certain λ's are possible for a standing wave Figure 7.12 Wave motion in restricted systems Wave-particle Duality Einstein remembered for E = mc2, where m = E/c2 = (hc/λ)/c2 = h/λc This appears to say that a photon of a certain wavelength has mass! Proved by Arthur Compton in 1922 E-M radiation is both waves & little packets of energy and matter called photons De Broglie 1923: if light has wave-particle duality, then matter, which is particle-like, must also be wavelike under certain conditions Rearranged m = h/c to get λ = h/mv This is called deBroglie wavelength. It means that all matter exhibits both particle and wave properties Sample Problem 7.4 (Note the relationship 1 Joule = 1 kg*m2/s2) Wave-particle Duality Bohr’s Theory: 1 e- in H atom occupying certain energy states - a certain quanta Spherical orbitals around the nucleus Chapter 7: Quantum Theory and Atomic Structure With de Broglie's hypothesis: e- must have a certain λ to make a complete revolution - like a standing wave An integral # of complete λ's to fit the sphere's circumference Circumference = 2 r, therefore nλ = 2 r, n = 1, 2, 3.... Figure 7.14 Summary of the major observations and theories leading from classical theory to quantum theory Heisenberg Uncertainty Principle: Uncertainty: (Δx)(mΔv) > h/4 Δx is the location of the electron mΔv is its momentum Need Δ because we can’t know both at the same time Sample Problem 7.4 (4th ed.): An electron moving near an atomic nucleus has a speed 6 x 106 ± 1% m/s. What is the uncertainty in its position (x)? WAVE FUNCTIONS & QUANTUM MECHANICS: Schrodinger developed Wave Functions, Ψ(psi), where Ψ2 is the probability of finding e- in a given space Led to 4 quantum numbers that describe the e-'s position in a complex equation: 1. Only certain wave functions are allowed 2. Each Ψn corresponds to an allowed energy for e- in atom 3. Thus energy of e- is quantized 4. Ψ has no physical meaning, but Ψ2 give the probability density 5. Allowed energy states are called orbitals 6. 3 integer #'s req'd to solve Ψ2 for 3-D space: n, l, ml Quantum Numbers and Atomic Orbitals An atomic orbital is specified by three quantum numbers. n = principal quantum number, a positive integer = 1, 2, 3,... - determines total E of e- in its electron shell - gives measure of prob distance from nucleus (orb size) - 2 or more e-s can be in same electron shell l = angular momentum or shape = < n - 1 , = 0,1,2,... - subshells w/in main shell, characterized by certain wave shapes 0 = s, 1 = p, 2= d, 3 = f, etc. ml = magnetic q.n. = +l, +l - 1, +l - 2, … 0, ... -l - specifies which orbital w/in a subshell e- is in - differ only in orientation, not shape Chapter 7: Quantum Theory and Atomic Structure (later we’ll do ms = spin q.n., +½ or -½ for each e-) Table 7.2 The Hierarchy of Quantum Numbers for Atomic Orbitals Sample Problem 7.5 Sample Problem 7.6 3-D shapes: Ψ21s – the 1s orbital is spherical. Ψ22s – the 2s orbital has some density close to nucleus and then another sphere farther away – a sphere within a sphere 2 Ψ 2p – the 2p orbitals have no probabilty of e- at the nucleus - called nodal plane Can be oriented in 3 directions of 3-D graph - x, y, z. 2px, 2py, 2pz have the 3 ml “names” +1, 0 and -1 Ψ23d – the 3d orbitals have 5 ml values, and each has 2 nodal surfaces, so they are in four sections. 3dxy, 3dxz, 3dyz, 3dx2-y2, 3dz2 2 Ψ 4f – the 4f orbitals have 7 ml values, 3 nodal surfaces Figure 7.15 Electron probability in the ground-state H atom Figure 7.16 The 1s, 2s and 3s orbitals Figure 7.17 The 2p orbitals Figure 7.18 The 3d orbitals Figure 7.19 One of the seven possible 4f orbitals You have to draw: Be able to draw 1s, 2s, 2p, and 3d orbitals. Practice now!