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# lecnotes03 - MIT OpenCourseWare http/ocw.mit.edu 5.111...

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MIT OpenCourseWare http://ocw.mit.edu 5.111 Principles of Chemical Science Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .

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________________________________________________________________________________ ________________________________________________________________________________ 5.111 Lecture Summary #3 Reading for today: Section 1.2 (1.1 in 3 rd ed ), and Section 1.4 (1.2 in 3 rd ed ) with a focus on pgs 10-12 in the 4 th ed or pgs 5-7 in the 3 rd ed . Read for Lecture 4: Section 1.5 (1.3 in 3 rd ed ) – The Wave-Particle Duality of Matter, and Section 1.6 (1.4 in 3 rd ed ) – The Uncertainty Principle. Topics: I. (Failure of) the classical description of an atom (continued from Lecture #2) II. Introduction to quantum mechanics: wave-particle duality III. Light as a wave, characteristics of waves IV. Light as a particle, the photoelectric effect I. (FAILURE OF) THE CLASSICAL DESCRIPTION OF AN ATOM Coulomb’s Force Law to describe the F between the nucleus and electron in an H atom. F(r) = -e 2 e = absolute value of an electron’s charge 4 π ε 0 r 2 r = distance between two charges ε 0 = permittivity constant of a vacuum ( 8.854 x 10 -12 C 2 J -1 m -1 ) electron Consider an H atom (Z=1) with 1 electron and 1 proton. When r → ∞ F(r) = ________ -e +e r As r 0 F(r) = ________ H nucleus The closer the electron is to the nucleus, the larger the attractive force between the two charges. The Coulomb force law tells us the force (F) as a function of r. The Coulomb force law does not tell us how r changes with ________________. There is a CLASSICAL EQUATION OF MOTION that tells us how the electron and nucleus move under influence of this Coulomb force: Newton’s 2 nd Law F = ma Force = mass times acceleration We can rewrite F as a function of velocity, F = m(_______) or distance, F = m(d 2 r/dt 2 ). We can plug in the Coulomb force law for F, and solve the equation for any r initial . If r initial is 10 Å (10 -10 m), a typical distance for an H atom, the calculation indicates that r = 0 at t = _______ sec!
This predicts that the electron should plummet into the nucleus in ______________ ! What is wrong here? It turns out that the laws of classical mechanics no longer work at this size scale.

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