Particle in a box: given the number of carbon atoms, and the wavelength. How do I...

Particle in a box: given the number of carbon atoms, and the wavelength. How do I find the highest filled orbital, the lowest unoccupied orbital, and the box length. (ex. # of C atoms = 4, wavelength = 508.9nm. HFO = ?, LUO= ?, Box length = ?nm

L=√[(hʎ/8mc) (n^2-n^2 )] I believe I need to use this equation to find the box length. I just don't know how to find what the n values are.

Expert Solution

Since this experiment only deals with unbranched hydrocarbons where the number of pi-electrons is equal to the total number of carbons in the system, thus for a system of 4 carbon atoms there will be 4 electrons. A system of unbranched hydrocarbons having 4 carbon atoms with 4 electrons corresponds to that of butadiene. Since each carbon is sp2 hybridized, each carbon has one unused p orbital. All the 4 p orbitals combine to form 4 -orbitals as shown below:

Each -orbital can accomodate 2 electrons. So 4 electrons can be accomodated in 2 -orbitals. Thus, n=2 for HFO and n=3 for LUO.

queen_honey_blossom answered 1 month ago

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