Question

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Physical Chemistry II Homework #4 CH3520 - Spring 2020 Exercise #11 (Total points: 40) Many proteins contain metal porphyrin molecules. The general structure of the porphyrin molecule is reported on the right. This molecule is planar and we can approximate the electrons as being confined inside a square. What are the first nine energy levels and degeneracies of a particle in a square of side a? Report the energy values in units of h/(8ma?) in increasing order. (25 points) The porphyrin molecule has 18 electrons. If we approximate the length of them what is its predicted lowest absorption energy? (FYI, experimentally one gets THz). (15 points) proximate the length of the molecule to 1000 pm, FYI, experimentally one gets roughly 510

Answer 1

The porphyrin ring, generally contains 26 pi electrons and the lowest absorption energy of electron from (4,2) to (4,3) energy level is 3.0153 * 10^(-19) J

Page : Date: Sol:- The porphyrin molecule is considered to planar and approximated as és being contined in La square of side a. for a particle in a 2-D (square) box :- | Energy (E) - (Man + my?) ?? Energy levels Degeneracy (h²8ma²) (4,3) (3,4) 25 (4,2) 12,41 20 (3,3) (114) (4,1) (1,4) (4,1) 2 Energy 27 20 1L Energy increases 1 clay (11 11c (1,2) 2 (2,1) 2 figure A

Page : Date: / Porphyrin molecule | As can be seen energy level is is given to possess 18 é o from figure A highest occupied (1,4) for (4) Lowest bus are excited fonds to : abeoxotion from eneran will be when eis 1,4 to (33) This corrent 18 - (9* +(332) - 41432+ (192) septem fina? I given a = 1000 pm = 1000 x 10 m = 10 m A&z - 16.626 X1034) 88 9.1 x 103'xtolla 0.603 X 16"" L : * This valuedoesnot_match your value in 'rolution- I The problem is that the porphyrin sina in total contains 26 le's and according to which the هفهعمعما معا وندل لهدی) (42) and Wher é from loccupies energy this level absorbs energy level (4,3), we get : AE 11 8 no 2 = 25 h² - 20 h² C 8ma2 = 5 x 16.626 X 1034)_ - 8x41x7o3 (109)2 - 5 h² 8ma? 3.0153 X10 -

Page : Date: / / et tettrou absorption energy from 3.0153 X10 I. Hence |(4,2) the lowest to (4,3) 19 is