* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Chapter 07
Relativistic quantum mechanics wikipedia , lookup
EPR paradox wikipedia , lookup
Interpretations of quantum mechanics wikipedia , lookup
History of quantum field theory wikipedia , lookup
Chemical bond wikipedia , lookup
X-ray photoelectron spectroscopy wikipedia , lookup
Symmetry in quantum mechanics wikipedia , lookup
Coupled cluster wikipedia , lookup
Hartree–Fock method wikipedia , lookup
Particle in a box wikipedia , lookup
Copenhagen interpretation wikipedia , lookup
Canonical quantization wikipedia , lookup
Double-slit experiment wikipedia , lookup
Hidden variable theory wikipedia , lookup
Astronomical spectroscopy wikipedia , lookup
Magnetic circular dichroism wikipedia , lookup
Bohr–Einstein debates wikipedia , lookup
Hydrogen atom wikipedia , lookup
X-ray fluorescence wikipedia , lookup
Matter wave wikipedia , lookup
Atomic theory wikipedia , lookup
Tight binding wikipedia , lookup
Theoretical and experimental justification for the Schrödinger equation wikipedia , lookup
Wave–particle duality wikipedia , lookup
Molecular orbital wikipedia , lookup
1 ATOMIC STRUCTURE Chapter 7 2 Excited Gases & Atomic Structure 3 Spectrum of White Light Line Emission Spectra of Excited Atoms • Excited atoms emit light of only certain wavelengths • The wavelengths of emitted light depend on the element. 4 5 Spectrum of Excited Hydrogen Gas Figure 7.8 6 Line Emission Spectra of Excited Atoms High E Short High Low E Long Low Visible lines in H atom spectrum are called the BALMER series. 7 Line Spectra of Other Elements Figure 7.9 8 The Electric Pickle • Excited atoms can emit light. • Here the solution in a pickle is excited electrically. The Na+ ions in the pickle juice give off light characteristic of that element. 9 Atomic Spectra and Bohr The classical view of atomic structure in early 20th century was that an electron (e-) traveled about the nucleus in an orbit. Paradox due to the classical view: 1. Any orbit should be possible and so is any energy. 2. A charged particle moving in an electric field should emit energy. Should end up falling into the nucleus ! 10 Atomic Spectra and Bohr Bohr said classical view was wrong. Needed a new theory — nowadays called OLD QUANTUM THEORY or OLD QUANTUM MECHANICS. e- can exist only in certain discrete orbits — called stationary states. e- is restricted to QUANTIZED energy states. 2 Energy of state = - C/n where n = quantum no. = 1, 2, 3, 4, .... 11 Atomic Spectra and Bohr Energy of quantized state = - C/n2 • Only orbits where n = integral no. are permitted. • Radius of allowed orbitals = n2 • (0.0529 nm) • But note — same eqns. come from a modern quantum mechanics approach. • Results can be used to explain atomic spectra. 12 Atomic Spectra and Bohr If e-’s are in quantized energy states, then ∆E of states can have only certain values. This explain sharp line spectra. 2 Atomic Spectra and Bohr E N E R G Y E = -C ( 1 / 2 ) 2 E = -C ( 1 / 1 ) n=2 n=1 Calculate ∆E for e- “falling” from a high energy level (n = 2) to a low energy level (n = 1). ∆E = Efinal - Einitial = -C[(1/nf2) - (1/ni)2], when nf=1 and ni=2: ∆E = -(3/4)C Note that the process is EXOTHERMIC ENERGY IS EMITTED AS LIGHT ! 13 ELECTROMAGNETIC RADIATION 14 15 Electromagnetic Radiation wavelength Visible light Amplitude wavelength Ultaviolet radiation Node 16 Electromagnetic Radiation Figure 7.1 17 Electromagnetic Radiation • Waves have a frequency • Use the Greek letter “nu”, , for frequency, and units are “cycles per sec” • • • • = c All radiation: • where c = velocity of light = 3.00 x 108 m/sec Long wavelength --> small frequency Short wavelength --> high frequency Electromagnetic Spectrum Long wavelength --> small frequency Short wavelength --> high frequency increasing frequency increasing wavelength 18 Electromagnetic Radiation 19 Red light has = 700 nm. Calculate the frequency. 1 x 10 -9 m 700 nm • = 7.00 x 10-7 m 1 nm 8 Freq = 3.00 x 10 m/s 7.00 x 10 -7 m 4.29 x 10 14 sec -1 20 Electromagnetic Spectrum Atomic Spectra and Bohr E N E R G Y E = -C ( 1 / 2 2 ) E = -C ( 1 / 1 2 ) n=2 n=1 ∆E = -(3/4)C C has been found from experiments (and is now called R, the Rydberg constant) R (= C) = 1312 kJ/mol or 3.29 x 1015 cycles/sec so, E of emitted light = (3/4)R = 2.47 x 1015 sec-1 and since = c/ = 121.6 nm This is exactly in agreement with experiment! 21 Origin of Line Spectra 22 Balmer series Figure 7.12 23 Atomic Line Spectra and Niels Bohr Niels Bohr (1885-1962) Bohr’s theory was a great accomplishment. Rec’d Nobel Prize, 1922 Problems with theory — • theory only successful for H. • introduced quantum idea artificially. • So, we go on to • MODERN QUANTUM MECHANICS or WAVE MECHANICS Quantization of Energy Max Planck (1858-1947) Solved the “ultraviolet catastrophe” CCR, Figure 7.5 24 25 Quantization of Energy An object can gain or lose energy by absorbing or emitting radiant energy in QUANTA. Energy of radiation is proportional to the frequency E = h• h = Planck’s constant = 6.6262 x 10-34 J•s 26 Photoelectric Effect Experiment demonstrates the particle nature of light. Photoelectric Effect Classical theory said that E of ejected electron should increase with increase in light intensity—not observed! • No e- observed until light of a certain minimum E is used. • Number of e- ejected depends on light intensity. A. Einstein (1879-1955) 27 Photoelectric Effect Understand experimental observations if light consists of particles called PHOTONS of discrete energy. PROBLEM: Calculate the energy of 1.00 mol of photons of red light. = 700. nm = 4.29 x 1014 sec-1 28 Energy of Radiation Energy of 1.00 mol of photons of red light. E = h• = (6.63 x 10-34 J•s)(4.29 x 1014 sec-1) = 2.85 x 10-19 J per photon E per mol = (2.85 x 10-19 J/ph)(6.02 x 1023 ph/mol) = 171.6 kJ/mol This is in the range of energies that can break bonds. 29 30 Quantum or Wave Mechanics de Broglie (1924) proposed that all moving objects have wave properties (mass)(velocity) = h / L. de Broglie (1892-1987) Note that this relation also applies to electromagnetic radiation: mc = h / , or h = mc , and since E = h and = c / , E = mc2 which is Einstein’s famous equation for the relation between mass and energy 31 Quantum or Wave Mechanics Baseball (115 g) at 100 mph = 1.3 x 10-32 cm Experimental proof of wave properties of electrons e- with velocity = 1.9 x 108 cm/sec = 0.388 nm Quantum or Wave Mechanics 32 Schrödinger applied the idea of ebehaving as a wave to the problem of electrons in atoms. He developed the WAVE EQUATION: HE whose solution gives the so-called WAVE FUNCTION, E. Schrodinger Describing an allowed state of energy 1887-1961 state E Quantization introduced naturally. WAVE FUNCTIONS, • (x) is a function of coordinates, x. • Each corresponds to an ORBITAL — the region of space within which an electron is found. • does NOT describe the exact location of the electron. • 2 is proportional to the probability of finding an e- at a given point. 33 Uncertainty Principle W. Heisenberg 1901-1976 Problem of defining nature of electrons in atoms solved by W. Heisenberg. Cannot simultaneously define the position and momentum (p= m•v) of an electron: x•p h/(2 ) If we determine the evelocity, precisely we can not determine the position very well and viceversa. 34 Types of Orbitals d orbital p orbital s orbital 35 Orbitals 36 • No more than 2 e- assigned to an orbital • Orbitals grouped in s, p, d (and f) subshells s orbitals d orbitals p orbitals 37 s orbitals p orbitals d orbitals s orbitals p orbitals d orbitals No. orbs. 1 3 5 No. e- 2 6 10 38 Subshells & Shells • Each shell has a number called the PRINCIPAL QUANTUM NUMBER, n • The principal quantum number of the shell is the number of the period or row of the periodic table where that shell begins. 39 Subshells & Shells n=1 n=2 n=3 n=4 QUANTUM NUMBERS The shape, size, and energy of each orbital is a function of 3 quantum numbers: n (major) ---> l (angular) ---> ml (magnetic) ---> shell subshell designates an orbital within a subshell 40 41 QUANTUM NUMBERS Symbol Values n (major) 1, 2, 3, ... l (angular) 0, 1, 2, ... n-1 Description Orbital size, energy, and # of nodes=n-1 Orbital shape or type (subshell) ml (magnetic) -l,...0,...+l Orbital orientation # of orbitals in subshell = 2 l + 1 42 Types of Atomic Orbitals Shells and Subshells When n = 1, then l = 0 and ml = 0 Therefore, in n = 1, there is 1 type of subshell and that subshell has a single orbital (ml=0 has a single value ---> 1 orbital) This subshell is labeled s (“ess”) Each shell has 1 orbital labeled s, and it is SPHERICAL in shape. 43 s Orbitals All s orbitals are spherical in shape. See Figure 7.14 on page 274 and Screen 7.13. 44 1s Orbital 45 2s Orbital 46 3s Orbital 47 48 p Orbitals When n = 2, then l = 0 and l = 1 Therefore, when n = 2 there are 2 types of orbitals — 2 subshells For l = 0 ml = 0, s subshell When l = 1, there is a NODAL PLANE For l = 1 ml = -1, 0, +1 this is a p subshell with 3 orbitals See Screen 7.13 p Orbitals • The three p orbitals are oriented 90o apart in space 49 50 2px Orbital 3px Orbital d Orbitals When n = 3, what are the values of l? l = 0, 1, 2 and so there are 3 subshells in the shell. For l = 0, ml = 0 ---> s subshell with single orbital For l = 1, ml = -1, 0, +1 ---> p subshell with 3 orbitals For l = 2, ml = -2, -1, 0, +1, +2 ---> d subshell with 5 orbitals 51 52 d Orbitals s orbitals have no planar node (l = 0) and so are spherical. p orbitals have l = 1, and have 1 planar node, and so are “dumbbell” shaped. This means d orbitals (with l = 2) have 2 planar nodes See Figure 7.16 53 3dxy Orbital 54 3dxz Orbital 55 3dyz Orbital 56 2 2 3dx - y Orbital 57 2 3dz Orbital