# One dimensional box

1. Apr 18, 2010

### Mechdude

1. The problem statement, all variables and given/known data

consider butadiene $H_2 C = CH-CH=cH_2$ and assume for simplicity that $\pi$ electrons move on a straight line (one -dimensional box) whose length l can be estimated as equal to two $C=C$ bond lengths (2*1.35 angstrom) , plus one $C-C$ lengths. Butadiene has four $\pi$ that fill the $n=1$ & $n=2$. the transition observed in a UV/VIS spectrum thus corresponds to the exitationof ane electron from the $n = 3$ state. Experimentally one finds that this corresponds to the absorption of light with a wavelengths of 217 nm. Compute and compare the lenghts of the 0ne-D box suggested by the sum of the bond length and by the energy of the transition.

2. Relevant equations

not sure

3. The attempt at a solution

not sure
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Apr 18, 2010

### nickjer

Well what are the energy levels of a 1D well with length L?

3. Apr 19, 2010

### Mechdude

$$E = \frac {n^2 h^2}{8 m l^2}$$
is that what im to use?
If it is may be energy is calculated from $E = hv$
and the information given then equate that to the energy difference calculated between n=3 and n= 2 ,
if im headed in the correct direction

4. Apr 19, 2010

### nickjer

Yes. You will want to find the L that gives that energy difference, and you will want to use the L given to you to find what energy difference that gets.

5. Apr 20, 2010

### Mechdude

thanks, nickjer.
regards.