Lecture 28 with notes

Lecture 28 with notes - Lecture 28 Chapter 39 The Bohr...

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Lecture 28 Chapter 39

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2 The energy of a hydrogen atom (equivalently its electron) changes when the atom emits or absorbs light: The Bohr model of the Hydrogen atom 39- Substituting f=c/ l and using the energies E n allowed for H: This is precisely the formula Balmer used to model experimental emission and absorption measurements in hydrogen! However, the premise that the electron orbits the nucleus is incorrect ! Must treat electron as matter wave. 22 low high 1 1 1 R nn     high low hf E E E   4 2 3 2 2 0 high low 1 1 1 8 me h c n n l   Where the Rydberg constant 4 7 -1 23 0 1.097373 10 m 8 me R hc
Determine the correct expression for the wavelength of light emitted when a hydrogen atom makes a transition from the n = 6 to the n = 2 energy level of the Bohr model. 3 1 2 3 4 5 10% 90% 0% 0% 0% 1. 1/ λ = R(1/36 1/4) 2. 1/ λ = R(1/4 1/36) 3. 1/ λ = 1/R (1/4 1/36) 4. 1/ λ = 1/R (1/4 1/36) 5. 1/ λ = R 2 (1/4 1/36)

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4 For light E ( x, y, z, t ) characterizes its wavelike nature, for matter the wave function Ψ ( x, y, z, t ) characterizes its wavelike nature. Schrö dinger’s Equation 38- Like any wave, Ψ ( x, y, z, t ) has an amplitude and a phase (it can be shifted in time and or position), which can be conveniently represented using a complex number a+ib where a and b are real numbers and i 2 = -1 . On the situations that we will discuss, the space and time variables can be grouped separately:     , , , , , it x y z t x y z e  where =2 p f is the angular frequency of the matter wave.
5 What does the wave function mean? If the matter wave reaches a particle detector that is small, the probability that that a particle will be detected there in a specified period of time is proportional to I ψ | 2 , where I ψ | is the absolute value (amplitude) of the wave function at the detector’s location. Schrö dinger’s Equation, cont’d 38- The probability per unit time interval of detecting a particle in a small volume centered on a given point in a matter wave is proportional to the value I ψ | 2 at that point. Since ψ is typically complex, we obtain I ψ | 2 by multiplying ψ by its complex conjugate ψ * . To find ψ * we replace the imaginary number i in ψ with –i wherever it occurs.

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This note was uploaded on 09/06/2010 for the course IE 111 taught by Professor Storer during the Spring '07 term at Lehigh University .

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Lecture 28 with notes - Lecture 28 Chapter 39 The Bohr...

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