PS2-08-Solution - Chem 442 Homework Set #2 - Solutions DUE:...

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Chem 442 Homework Set #2 - Solutions DUE: Thursday, Nov. 6. 2008 1) (McQ&S 3-3) ( ) ( ) () 2 22 2 2 ˆ The eigenvalue equation is where c is a constant. ˆ a) cos cos ; ˆ b) ; ˆ c ) ( 2 3 ) 23 it xx Af x cf x d Af x x x f x eigenvalue dx d Af x e i e i f x eigenvalue i dt dd 2 A fx e e dx dx eigen ωω αα ωωωω ω = == = = = = =+ + = + + = + + 2 26 ˆ d) , 6 6 , ; 6 yy value A f xy xe f xy e igenva lue y =++ = = 2) (McQ&S, 3-6) Hexatriene ()()( ) Page 83 in McQ&S: Approximate C-C bond length as 154pm, C=C 135pm, C atom radius=77pm. Hexatriene has 2 C-C bonds and 3 C=C bonds and two C atom radii at the ends. Total length = L= 2 154 3 135 2 77 867 p ++ = ( ) 2 34 2 19 2 2 31 12 The six electrons fill the lowest 3 energy levels (n=1,2,3). The lowest energy transition will be from n=3 to n=4. 6.626 10 h E= 16 9 5.61 10 8 8 9.109 10 867 10 5.61 1 fi e m Js nn J mL kg m E π −− ×⋅ Δ− = = × ×× Δ= × 22 1 19 4 1 5.034 10 02 . 8 2 1 0 1 cm Jc m J × ×= × Problem Set #2 Solution - 1 -
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3) (MQ&S, 3-28) A particle on a ring must have some amplitude (could be 0) at every angle . If the particle starts at one value and then travels around the ring to +2 , it must have the same amplitude as when it θ θθ () ( ) () 2 started at , otherwise the particle will interfere with itself and eventually end up with zero amplitude everywhere. Hence, 2 are the appropriate boundary conditions.
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PS2-08-Solution - Chem 442 Homework Set #2 - Solutions DUE:...

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