A porphyrin ring is a nolecule which is prcsent in chlorophyll, hemo- globin, aud other important conpounds. Some aspects of the physics of its inolecular properties can be describel by representing it as a one- dimcusional circular path of radius r = 4 Å, aloug which 18 clectrous are Coustraiued to move. (a) Write down the normalized one-particle energy eigenfunctions of the systein, assuming that the electrons do not interact with each other. (b) How many electrons are there in each level in the ground state of the molecule? (c:) What is the lowest electronic excitation energy of the molecule? What is the corresponding wavelength (give a numerical value) at which the molecule can absorb radiation?
A porphyrin ring is a nolecule which is prcsent in chlorophyll, hemo- globin, aud other important conpounds. Some aspects of the physics of its inolecular properties can be describel by representing it as a one- dimcusional circular path of radius r = 4 Å, aloug which 18 clectrous are Coustraiued to move. (a) Write down the normalized one-particle energy eigenfunctions of the systein, assuming that the electrons do not interact with each other. (b) How many electrons are there in each level in the ground state of the molecule? (c:) What is the lowest electronic excitation energy of the molecule? What is the corresponding wavelength (give a numerical value) at which the molecule can absorb radiation?
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Transcribed Image Text:A porphyrin ring is a inolecule which is prcsent in chlorophyll, hemo-
globin, aud other important conpounds. Some aspects of the physics
of its inolecular properties can be describel by representing it as a one-
dimcusional circular path of radius r = 4 Å, aloug which 18 clectrons are
COustraiued to move,
(a) Write down the normalized one-particle energy eigenfunctions of the
systein, assuming that the electrons do not interact with each other.
(b) How many electrons are there in each level in the ground state of
the molecule?
(c:) What is the lowest electronic excitation energy of the molecule?
What is the corresponding wavelength (give a numerical value) at which
the molecule can absorb radiation?
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