How do I calculate the length of a bond?

[fizzicsdummy]

“In C6H8, the carbon atoms are connected in a chain. In a rough approximation, some electrons can be viewed as confined to a line with the length of this chain. C6H8 absorbs ultraviolet light with wavelength 357 nm, which causes an electron to change from the third lowest allowed energy to the fourth lowest allowed energy. Use this information to estimate the length in pm of a typical carbon-carbon bond in C6H8.”

I assume I could just calculate the radius of a carbon atom and multiply it by 2 to find a rough estimate of the length of a carbon-carbon bond. However, I don't know how to do this and I don't know the importance of the energy level change described in the problem. I'd really appreciate help understanding this. An equation (if one exists) would also be appreciated. I do know that radius = (n^2)(Bohr radius). Thanks!

 

[GCT]

“In C6H8, the carbon atoms are connected in a chain. In a rough approximation, some electrons can be viewed as confined to a line with the length of this chain. C6H8 absorbs ultraviolet light with wavelength 357 nm, which causes an electron to change from the third lowest allowed energy to the fourth lowest allowed energy. Use this information to estimate the length in pm of a typical carbon-carbon bond in C6H8.”

I assume I could just calculate the radius of a carbon atom and multiply it by 2 to find a rough estimate of the length of a carbon-carbon bond. However, I don't know how to do this and I don't know the importance of the energy level change described in the problem. I'd really appreciate help understanding this. An equation (if one exists) would also be appreciated. I do know that radius = (n^2)(Bohr radius). Thanks!

You can estimate the length of the bond by referring to the typical bond energies of carbon - carbon bonds e.g. single , double , triple and compare these with the energy of the wavelength given to you.

The other way is by using the Particle In a Box theory , this is better than using the Bohr model , however it depends on which class you are in.