Quantum Mechanics Reading:Gray:(1-8)to (1-12) OGC:(4.4)to(4.5) 1-1
Reading: Gray: (1–8) to (1–12) OGC: (4.4) to (4.5) II-1
A Timeline of the Atom -400BC...0 1800 1850 1900 1950 400 B.C.Democritus:idea of an atom 1808 John Dalton introduces his atomic theory. 1820 Faraday:charge/mass ratio of protons 1885 E.Goldstein:discovers a positively charged sub-atomic particle 1898 J.J.Thompson finds a negatively charged particle called an electron. 1909 Robert Millikan experiments to find the charge and mass of the electron. 1911 Ernest Rutherford discovers the nucleus of an atom. 1913 Niels Bohr introduces his atomic theory. 1919 The positively charged particle identified by Goldstein is found to be a proton. 1920s Heisenberg,de Broglie,and Schrodinger. 1932 James Chadwick finds the neutron. 1964 The Up,Down,and Strange quark are discovered. 1974 The Charm quark is discovered. 1977 The Bottom quark is discovered. 1995 The Top (and final)quark is discovered. -2
A Timeline of the Atom 400 BC 0 1800 400 B.C. Democritus: idea of an atom 1808 John Dalton introduces his atomic theory. 1820 Faraday: charge/mass ratio of protons 1885 E. Goldstein: discovers a positively charged sub-atomic particle 1898 J. J. Thompson finds a negatively charged particle called an electron. 1909 Robert Millikan experiments to find the charge and mass of the electron. 1911 Ernest Rutherford discovers the nucleus of an atom. 1913 Niels Bohr introduces his atomic theory. 1919 The positively charged particle identified by Goldstein is found to be a proton. 1920s Heisenberg, de Broglie, and Schrödinger. 1932 James Chadwick finds the neutron. 1964 The Up, Down, and Strange quark are discovered. 1974 The Charm quark is discovered. 1977 The Bottom quark is discovered. 1995 The Top (and final) quark is discovered. ...... ....... 1850 1900 1950 II-2
The Person Behind The Science Werner Heisenberg 1901-1976 Highlights Studied under Max Born,James Franck, and Niels Bohr Received Nobel Prize in Physics(1932)for "for the creation of quantum mechanics..." Moments in a Life With his help,the Max Planck Institute for Physics is founded (1948) Publishes his theory on quantum mechanics (1925,at the age of 23!) Ⅱ-3
The Person Behind The Science Werner Heisenberg 1901-1976 With his help, the Max Planck Institute for Physics is founded (1948) Publishes his theory on quantum mechanics (1925, at the age of 23!) Moments in a Life Highlights Studied under Max Born, James Franck, and Niels Bohr Received Nobel Prize in Physics (1932) for “for the creation of quantum mechanics…” II-3
The Modern Picture of the Hydrogen Atom Bohr Model Current Model e(=0) ●e(t=2)e(t=0) r e(t=1) 。e(t=5)●et=4) r ●● e(t=3) ●e(te1) e~(t=2) ●e(t=6) △x=0;△p=0 so△x△p=0<h! 4元 The uncertainty in an electron's The Bohr model violates position is comparable to the the uncertainty principle! diameter of the atom itself. 4
e- (t=0) r r The Bohr model violates the uncertainty principle! The Modern Picture of the Hydrogen Atom e- (t=1) e- (t=0) e- (t=1) e- (t=4) e- (t=2) e- (t=3) e- (t=5) e- (t=6) The uncertainty in an electron’s position is comparable to the diameter of the atom itself. Bohr Model Current Model Δx = 0; Δp = 0 so ΔxΔp = 0 < ! e- (t=2) h 4 π II-4
Uncertainty in Electron Momentum and Position We want Ax =10-11 m (i.e.,0.1 A) h ApAX≥4 △P24元·△X 6.6×10-34Js △p≥ 12.6×10-11m =5.3x10-24kgms1 How big is this uncertainty? △p=m。·△vso △V= △P me 10-2kg.m.s- 1030kg =107ms1 Suppose we look for the electron again after only 1x10-14 s: △x=(10m·s)(10-14s)=10-7m=1000A!
Uncertainty in Electron Momentum and Position e– ? ? We want Δx ≈ 10-11 m (i.e., 0.1 Å) ΔpΔx ≥ so Δp ≥ = 5.3x10– 24 kgms-1 How big is this uncertainty? Suppose we look for the electron again after only 1x10-14 s: h 4π h 4π • Δx Δp = me • Δv so Δv = Δp me Δv ≈ 10−23 kg• m• s−1 10−30 kg = 107 m• s−1 Δx = (107 m • s−1 )•(10−14 s) = 10−7 m = 1000Å! Δp ≥ 6.6 × 10−34J⋅ s 12.6 × 10−11m II-5
The Modern Picture of an Atom 0.11 0.18 ● 0.32 0.05 The best we can do is say what the probability of finding an electron is at any given point for any individual observation Such information is described by a function with properties of a wave,hence the name WAVEFUNCTION Π-6
The Modern Picture of an Atom The best we can do is say what the probability of finding an electron is at any given point for any individual observation Such information is described by a function with properties of a wave, hence the name WAVEFUNCTION 0.11 0.18 0.32 0.05 II-6
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Waves in 1-D 0 d For this example, But f also varies with time y=f(x)=A sin X d y f(x,t)=A sin d cos(ωt) The function is called the Wavefunction: 平xt) Π-8
Waves in 1–D A d For this example, But f also varies with time The function is called the Wavefunction: Ψ(x,t) 0 y= f(x) = A sin ( πx d ) y = f(x,t) = A sin cos (ωt) ( πx d ) II-8
Boundary Conditions to Define Allowed Waves: 1)Tie the Ends Down 2)Find a Standing Wave in the Box Allowed Standing Wave Ends are fixed at =0 always Not an Allowed Wave Not Even a Standing Wave Ends not Tied Down A Traveling Wave L-9
Allowed Standing Wave Ends are fixed at Ψ = 0 always Not an Allowed Wave Ends not Tied Down Not Even a Standing Wave Boundary Conditions to Define Allowed Waves: 1) Tie the Ends Down 2) Find a Standing Wave in the Box A Traveling Wave II-9
Nodes ThisΨhas No Nodes There are no points for which=0 at all times (The ends were fixed by the boundary conditions and therefore don't count as nodes) L-10
Nodes There are no points for which Ψ = 0 at all times (The ends were fixed by the boundary conditions and therefore don’t count as nodes) This Ψ has No Nodes II-10
