kingwinner
10-01-06, 09:49 PM
http://www.geocities.com/asdfasdf23135/chem1.JPG
I have many questions about this problem...I don't understand it at all...It would be nice if someone can explain and guide me through this problem. Any help is appreciated. :)
1. How can something have 22 "pi" electrons?
2. What is the meaning of effective length?
3. Why can this problem be modelled by the "particle in a 1D box model"? Energy levels are not 1D...
4. What is the length of the 1D box?
5. Why is the lowest energy absorption from the 11th energy level to the 12th energy level? (how can I know?)
James R
10-02-06, 12:22 AM
What level are you studying at? Are you trying to teach yourself quantum physics and chemistry, or are you taking a course?
1. How can something have 22 "pi" electrons?
Chances are that this is referring to electrons in pi orbitals, which refers to a particular type of chemical bond.
2. What is the meaning of effective length?
The polyene is not a molecule which exists in a straight line. It is probably bent in some way. Therefore, measuring its length in one dimension becomes a little problematic.
3. Why can this problem be modelled by the "particle in a 1D box model"? Energy levels are not 1D...
What makes you say that energy levels are not 1D? Energy is a scalar quantity.
Also, what aspect of the molecule do you think is being modelled here? That is, you need to decide what the "box" corresponds to. And what particles are in the box.
4. What is the length of the 1D box?
I'd guess 1.86 nm.
5. Why is the lowest energy absorption from the 11th energy level to the 12th energy level? (how can I know?)
I think they are assuming that 2 electrons occupy each energy level in the molecule. Therefore, the electrons in the highest energy level are in the n=11 level. The lowest level absorpsion is then from n=11 to n=12, since the levels are equally spaced.
geodesic
10-02-06, 03:33 PM
The lowest level absorpsion is then from n=11 to n=12, since the levels are equally spaced.Erm, no. Energy levels in a 1D box scale by n^2, so lower energy levels are closer together. The gap between the eleventh and twelfth energy levels is still the smallest though.
http://upload.wikimedia.org/math/c/f/2/cf246592053c9e29ba3a80e14ba220bc.png