One-Dimensional Box: Analyzing Butadiene's UV/VIS Spectrum

[Mechdude]

Homework Statement

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.

Homework Equations

not sure

The Attempt at a Solution

not sure

 

[nickjer]

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

 

[Mechdude]

$$E = \frac {n^2 h^2}{8 m l^2}$$
is that what I am 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 I am headed in the correct direction

 

[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.

 

[Mechdude]

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.

thanks, nickjer.
regards.