Lecture12_AtomicStructure2

Lecture12_AtomicStructure2 - Physics 126 Lecture 12 March...

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S. Du Sp2011 1 Physics 126 Lecture 12 March 18, 2011 Atomic Structure Energy Levels and Spectra Correspondence Principle Nuclear Motion Atomic Excitation Laser Reading: Chap 4: 4.5 – 4.9 Shengwang Du
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S. Du Sp2011 2 Review of the Bohr Model n r n π λ 2 = p h = h n L = hypothesis (postulate) 0 2 2 0 2 2 a n me h n r n = = ε 2 2 2 0 4 0 2 1 8 8 n h me r e E n n πε = = A m me h a 5 . 0 10 292 . 5 11 2 0 2 0 = × = =
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S. Du Sp2011 3 The total energy E is thus quantized due to quantization of r n =a 0 n 2 Since the total energy of a circular orbit is The state with n =1 has the lowest energy and it is called the ground state. The ground state of H atom has E 1 = -13.6 eV ; r 1 = a 0 . When n = , r = , E = 0, i.e. the electron is unbound. Thus |E n | is the energy needed to ionize an electron in a state n. |E n | is also called the binding energy. Quantization of Energy Levels in Bohr Model 2 2 ke E r =− 2 22 2 1.44 1 13.6 2 0.1018 n o ke eV nm eV E an nm n n 0 4 1 πε = k
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S. Du Sp2011 4 Ground state Excite states Free electron (E>0)
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S. Du Sp2011 5 In the Bohr model how do atoms absorb and emit energy? Additional Postulate Needed (www.colorado.edu/physics/2000/quantumzone/bohr.html) Bohr uses the Planck energy Quanta h ν
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S. Du Sp2011 6 An electron in a stationary state n does not radiate. But it can emit a photon when it “jumps” from a higher energy state n 1 to a lower energy state n 2 . The energy of the emitted photon is assumed to be: Rydberg constant ( R = 1.097x10 7 m -1 ) Postulate on Transition between Stationary States: Frequency of light emitted (absorbed) determined by energy difference divided by h Perfect Agreement with experiment! 22 2 4 2 2 2 2 11 2 n o ke ke mk e E an n n ke m =− h h 24 12 322 21 =( ) / 2 ( )( - ) 4 mk e EE nn νπ π −= h h 32 2 1 =( ) / 2 ( )( - ) 4 mk e c cc n n ν λπ = h h 3 . 6 cR e V =
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S. Du Sp2011 7 ± Lyman series (in UV) result from transition from excited states to the ground state. (i.e. with n = 1) ± Balmer series (visible) result from transition from excited states to the the 1 st excited state. (i.e. with n = 2) Balmer Hydrogen Spectra Series Emission spectrum Absorption spectrum
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S. Du Sp2011 8 Balmer series (Visible) ,... 5 , 4 , 3 1 2 1 1 2 2 = = n n R λ Emission lines of hydrogen atoms Lyman series (UV) ,..... 4 , 3 , 2 1 1 1 1 2 2 = = n n R ,... 6 , 5 , 4 1 3 1 1 2 2 = = n n R Paschen series (Infrared) hc E R 1 =
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S. Du Sp2011 9 Ritz combination principle ± Certain frequencies in the emission spectrum can be summed to give other frequencies. ± This can be understood when we consider a transition from n 3 to n 2 is followed by a transition from n 2 to n 1 , in terms of frequencies n, we have: = = 2 2 2 1 2 3 2 2 1 1 1 1 n n cR n n cR n1 n2 n2 n3 ν n1 n3 n1 n2 n2 n3 = = + 2 3 2 1 1 1 n n cR The principle is just an observation of the fact that energies of excited states can be emitted by one step or multiple steps.
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S. Du Sp2011 10
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Lecture12_AtomicStructure2 - Physics 126 Lecture 12 March...

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