PS3-08-Solution - Chem 442 Homework Set #3 - Solutions DUE:...

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Chem 442 Homework Set #3 - Solutions DUE: Friday, November 7, 2008 1) a) McQ&S, 3-26 () 2 2 2 2 222 2 2 2 2 2 22 2 2 2 2 2 The energy levels for the particle in the 3-D box are: plug in a=b=1.5c 8 8 /1.5 2.25 8 xyz x y x z nnn y x z y x z nn n n n h E ma b c n n n h E ma a a n n n h E a E ⎛⎞ =+ + ⎜⎟ ⎝⎠ + + 2 2 2 2 2 2 1,1,1 2 2 2,1,1 1,2,1 2 2,2,1 2 1,1,2 2.25 8 In units of , the first four energy levels are 8 1 1 2.25 1 4.25 2 1 2.25 1 1 2 2.25 1 7.25 2 2 2.25 1 10.25 112 . 2 5 2 1 1 The dege yz nx y z h n ma h ma E EE E E + + = == + + = + + = + = + = neracies are 1,2,1,1 respectively. b) () () 2 22 2 2 2 2 34 2 31 10 2.25 2.25 8 First excited state: 2, 1, 1 6.626 10 2 1 2.25 1 1 1 2.25 1 8 9.11 10 5.00 10 photon f i i f photon xi yi zi xf yf zf e xy z photon E E E E h En n n n n n ma Js E kg m −− =−Δ =− = + = ×⋅ + ×× Problem Set #3 Solution - 1 -
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() ( ) ( ) 2 34 19 2 31 10 19 34 15 1 15 6.626 10 417 7 . 2 3 71 0 8 9.1 10 5.00 10 / 7.237 10 / 6.626 10 1.09 10 1.09 10 photon Js EJ kg m Eh v vEh J J s vs H z −− ×⋅ =− ×× =→ = = × × = × 2) McQ&S, C-4 2*2 4*4 2* 5 4 16 10 0 cos 0 , and the vectors are orthogonal. 2 AB AB AB SO θ π ⋅= + − + − −=− + = = = 3) a) McQ&S, 4-6 () () * 0 22 2 1/2 2 2 92 3 4 2 3 9 2 9 ˆ ˆ where , in this problem, 0 2 630 ˆ 2 630 2 2 630 264 2 630 2 2 a EH d x d HV x V x mdx d Hx a x ma d x d ax ax x d x d xa ax x d x a ψψ ψ = + = ⎛⎞ ⎜⎟ ⎝⎠ + + = = = = = ( ) 2 2 99 0 2 3 4 2 2 9 0 2 42 33 24 9 0 52 4 5 6 12 12 630 630 21 2 2 630 2 2 12 12 2 630 (2 12 12 4 24 2 24 2 12 12 ) a a a ax x Ex a x a a x x am a Ea x a x x a a x x d x x a x a x a x a x ax a x ax x dx −+ ⎡⎤ + ⎢⎥ ⎣⎦ + + + + −+−+ = = = 2 d x Problem Set #3 Solution - 2 -
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2 6 5 24 33 42 9 0 22 3 76 5 43 9 0 7 92 2 2 2* 2 0 630 (12 36 38 16 2 ) 2 630 12 36 38 16 2 27 654 3 630 12 36 38 16 2 630 2 2 7 6 5 4 3 2 105 6 ˆ a a a E x ax a x a x a x dx ma aa Ex x x x Ea E ma EH d x ψψ =− + +
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This note was uploaded on 02/12/2011 for the course CHEMISTRY 442 taught by Professor Lizzy during the Spring '10 term at Hanoi University of Technology.

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PS3-08-Solution - Chem 442 Homework Set #3 - Solutions DUE:...

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