Homework 5 Key

Homework 5 Key - CHEMISTRY 201X: Homework #5 "Wavefunctions...

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CHEMISTRY 201X: Homework #5 Due : Monday, October 15, 2007 -1- “Wavefunctions and Electronic Transitions” (1) (8 pts) Using the Bohr model for the hydrogen atom, (a) (2 pts) Derive an expression for the speed v n of an electron in orbit n in terms of h , m , and e , where h is Planck’s constant, m and e are the mass and charge of the electron. 22 2 nn n nh h nh 2 π e1 mvr = ; r = n ; v = = 2 π 4 π me 2 π mr h n (b) (2 pts) Calculate the speed (in m/sec) of an electron in the ground state and the two lowest excited states of the H atom. One challenge is to obtain the factor 2 π e h in units m/sec. We can use the Rydberg to help us here: 24 -18 2 2 π me 2.18×10 J = h . Therefore, ⎛⎞ ⎜⎟ ⎝⎠ 1/2 2 4 -18 2 -18 6 2- 3 1 π . 0 9 × 1 0 J 2 π . 0 9 × 1 0 J = and =2 .19×10 m /sec hm h 9 . 1 1 × 1 0 k g n = 1: () 66 1 1 v = 2.19×10 m/sec = 2.19×10 m/sec 1 n = 2: 2 1 v = 2.19×10 m/sec = 1.09×10 m/sec 2 n = 3: 65 3 1 v = 2.19×10 m/sec = 7.29×10 m/sec 3 (c) (2 pts) In a transition from the ground state of H that involves moving an electron through a distance that is approximately equal to the orbit diameter of the ground state, what characteristic time would be required for the transition? Orbit diameter of the ground state is 2r 1 = 2(0.529 Å) = 1.058 × 10 10 m Time = Distance / Speed = (1.058 × 10 10 m) / (2.19 × 10 6 m/sec) = 4.83 × 10
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This homework help was uploaded on 03/27/2008 for the course CHEM 201 taught by Professor Miller during the Fall '07 term at Iowa State.

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Homework 5 Key - CHEMISTRY 201X: Homework #5 "Wavefunctions...

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