Ultraviolet radiation and radiation of shorter wavelengths can damage biological molecules because they carry enough energy to break bonds within the molecules. a typical carbon–carbon bond requires 348 kj> mol to break. what is the longest wavelength of radiation with enough energy to break carbon–carbon bonds?

Longest wavelength :3.44 x 10⁻⁷ m

Explanation:

The  maximum wavelength of the radiation  with enough energy to break carbon to carbon bonds will be given by:

                        E= hc/λ    where h is Plancks constant for one photon,

                                                     c speed of light

                                                      E enrgy required  per mol

One has to be careful in this problem to either multiply Planck`s constant by Avogadro's  number to obtain the energy of a mol of photons or convert the given required energy  per mol to energy per atom.

Substituting in our equation and doing the calculations:

λ = hc/E

λ = 6.626 x 10⁻³⁴ Js /mol x 3 x 10^8 m/s  x 6.022 x 10²³8 mol  / ( 3.48 x 10⁵ J    =  3.44 x 10⁻⁷ m = 3440 nm which corresponds to the Infrared part of the spectrum.